Cranks can be easily identified as those who believe in Georg Cantor's gibberish.

[Eram semper recta]

Cantor was right in saying that the mythical set of real numbers is uncountable, but not for the reasons he thought!

The "set of real numbers" is uncountable because its members cannot be systematically listed. Most of the members don't even exist!

Defn: A set is countable if its members can be systematically named.

Other definitions:

A set is countable if its members can be indexed.
(This is similar to saying: A set is countable if its members can be placed into a bijection with |N or a subset of |N).

Why is |N itself countable? Because the members of |N can be systematically NAMED using any radix system.

A set is countable if its members can be systematically listed.

Now Wolfgang Mueckeheim will talk about ALL the members but this is not what Cantor meant - even if Cantor did say ALL. Cantor was delusional but not so stupid as to mean ALL members.

Cantor's DIAGONAL (mis) ARGUMENT is the joke of the 20th century. In it, Cantor assumes that every "real number" (no such thing!) has an "infinite decimal expansion" which is FALSE.

However, if one accepts that every "real number" (no such thing!) has a mythical "infinite decimal expansion", then the set (0,1) can be systematically named as demonstrated in my video:

https://youtu.be/hlqTuuhR3-4

Since set (0,1) is equipollent to (-oo, oo), it follows that the set (-oo, oo) is therefore countable. Q.E.D.

Mainstream mathematics academics are far too stupid to match my insight and depth of understanding. I am the greatest mathematician alive today. This is not a delusion, but a FACT.

Yes, I do know better!

[Eram semper recta]

A **NUMBER** is a **NAME** given to a **MEASURE** that describes a **MAGNITUDE** or **SIZE**.

[Brain Deitke]

Eram semper recta wrote:

> Cantor was right in saying that the mythical set of real numbers is
> uncountable, but not for the reasons he thought!
>
> The "set of real numbers" is uncountable because its members cannot be
> systematically listed. Most of the members don't even exist!

nevermind this nonsense, answer this simple question.

If the vaxx cant stop you from spreading and getting infected with the
invisible, undetected "virus", why the need of *covid_passport*?? Let's
see how your brain is hardwired. So we can establish an IQ.

[Dan Christensen]

STUDENTS BEWARE: Don't be a victim of JG's fake math

On Saturday, August 21, 2021 at 8:12:07 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

>
> Mainstream mathematics academics are far too stupid to match my insight and depth of understanding. I am the greatest mathematician alive today. This is not a delusion...

It kind of is, Troll Boy.

JG here claims to have a discovered as shortcut to mastering calculus without using limits. Unfortunately for him, this means he has no workable a definition of the derivative of a function. It blows up for functions as simple f(x)=|x|. Or even f(x)=0. As a result, he has had to ban 0, negative numbers and instantaneous rates of change rendering his goofy little system quite useless. What a moron!

Forget calculus. JG has also banned all axioms because he cannot even derive the most elementary results of basic arithmetic, e.g. 2+2=4. Such results require the use of axioms, so he must figure he's now off the hook. Again, what a moron!

Even at his advanced age (60+?), John Gabriel is STILL struggling with basic, elementary-school arithmetic. As he has repeatedly posted here:

"There are no points on a line."
--April 12, 2021

"Pi is NOT a number of ANY kind!"
--July 10, 2020

"1/2 not equal to 2/4"
--October 22, 2017

“1/3 does NOT mean 1 divided by 3 and never has meant that”
-- February 8, 2015

"3 =< 4 is nonsense.”
--October 28, 2017

"Zero is not a number."
-- Dec. 2, 2019

"0 is not required at all in mathematics, just like negative numbers."
-- Jan. 4, 2017

“There is no such thing as an empty set.”
--Oct. 4, 2019

“3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
--Oct. 22, 2019

No math genius our JG, though he actually lists his job title as “mathematician” at Linkedin.com. Apparently, they do not verify your credentials.

Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

[Michael Moroney]

On 8/21/2021 10:31 AM, Dan Christensen wrote:
> STUDENTS BEWARE: Don't be a victim of JG's fake math
>
> On Saturday, August 21, 2021 at 8:12:07 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:
>
>>
>> Mainstream mathematics academics are far too stupid to match my insight and depth of understanding. I am the greatest mathematician alive today. This is not a delusion...
>
> It kind of is, Troll Boy.
>

"Kind of" ????

[Brain Deitke]

you guys look confused like a LGBTQ+, I don't know what happens your
countries.

[Eram semper recta]

Anonymous coward and king troll of sci.math Dan Christensen spammed:

> "There are no points on a line."

Lie. I never said that. What I did say is that a line does not consists of points. When we talk about points on a line, we really mean distances that are indicated much like road signs do for distances travelled along a road.

A line is one of innumerable distances between any two points.
A straight line is the shortest distance between two points.

> "Pi is NOT a number of ANY kind!"

True. Pi is merely a symbol for an incommensurable magnitude - apparently a concept too advanced for an imbecile like Dan Christensen.

> "1/2 not equal to 2/4"

Lie. I have NEVER said this. What I have talked about is the difference in the process of measure.
What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.

There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:

_ / _ _
_ _ / _ _ _ _

The length _ is not equal to the length _ _ .

> “1/3 does NOT mean 1 divided by 3 and never has meant that”

True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

Also, my article on pi not being a number of any kind:

https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3

The true story of how we got numbers:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

No such thing as a "real number" or a "real number line":

https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc

There is no valid construction of "real number" - it's a myth:

https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU

> "3 =< 4 is nonsense.”

True. In mathematics, it is called an invalid disjunction.

3 <= 4 means EITHER 3 < 4 OR 3 = 4

Actually, there is no "OR" part, so the logical disjunction is invalid.

> "Zero is not a number."

True. While not a number of any kind, it is very useful in mathematics.

https://drive.google.com/file/d/1w2tt7IgoIu-ychDCoYi-4jOAzToy0ViM

> "0 is not required at all in mathematics, just like negative numbers."

Half-truth. While negative numbers are not required in mathematics, they are extremely useful.

> “There is no such thing as an empty set.”

True. Even the father of all mainstream mathematical cranks rejected the idea of empty set. But let's not go too far ... there isn't even a definition of "set" in set theory!

https://youtu.be/KvxjOMW6Q9w

https://youtu.be/1CcSsOG0okg

> “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)

True. These are propositions that are implied by the given equations. For example, my historic geometric identity states:

[f(x+h)-f(x)]/h = dy/dx + Q(x,h)

And so, f(x+h)-f(x)]/h <=> dy/dx + Q(x,h)

The theorem:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

How it provides a rigorous definition of integral for the flawed mainstream calculus:

https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

The day will come when this vicious anonymous troll Dan Christensen is convicted in a court of law.

Download for free the most important mathematics book ever written:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view

[Eram semper recta]

On Saturday, 21 August 2021 at 08:12:07 UTC-4, Eram semper recta wrote:

Refreshed due to troll activity.

[zelos...@gmail.com]

All the memebers of R exists and the set of R is easily constructed so tough shit, you are wrong

[Eram semper recta]

Afraid not. Do you want to try again? LMAO.

My argument is more solid than any diamond. It exposes your ignorance and shame without mercy.

[zelos...@gmail.com]

They are, so tough shit :)

Your argument is is like dust, it has no structure ot it.

[Eram semper recta]

And yet ... you cannot refute one iota of it. :)

[Dan Christensen]

On Saturday, August 21, 2021 at 4:16:57 PM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

STUDENTS BEWARE: Don't be a victim of JG's fake math

> > "1/2 not equal to 2/4"
> Lie. I have NEVER said this.

A direct quote from October 22, 2017 here at sci.math

> What I have talked about is the difference in the process of measure.
> What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
> 2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.
>
> There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:
>

When will you learn, Troll Boy? 1/2 is ALWAYS EQUAL to 2/4.

[snip]

> > “1/3 does NOT mean 1 divided by 3 and never has meant that”

> True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail...

If you can't dazzle them brilliance, baffle them with bullshit, right, Troll Boy?

> > "3 =< 4 is nonsense.”
> True. In mathematics, it is called an invalid disjunction.
>

Nothing "invalid" about it, Troll Boy.

> 3 <= 4 means EITHER 3 < 4 OR 3 = 4
>

It means 3 < 4 OR 3 = 4, which is always truly.

See: https://en.wikipedia.org/wiki/Truth_table#Logical_disjunction_(OR)

[snip]

> > "Zero is not a number."
> True. While not a number of any kind, it is very useful in mathematics.
>

It really is a number, Troll Boy. Deal with it.

> > "0 is not required at all in mathematics, just like negative numbers."

> Half-truth.

Nope. Completely false.

> While negative numbers are not required in mathematics, they are extremely useful.

<yawn!>

> > “There is no such thing as an empty set.”

> True.

Umm... What about the set of all your brilliant mathematical discoveries? Empty.

[snip]

> > “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions”

> True.

Nope. The biconditional is logical connective. See https://en.wikipedia.org/wiki/Logical_biconditional

3 is not a logical proposition or a statement that is true or false. 3 is a number. So 3 <=> 2+1 would be an error in syntax. Deal with it, Troll Boy.


[snip]

> > Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at

https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Also, all direct quotes from you, Troll Boy. To the extent that you will be remembered at all, history will not be kind to you. Time to cut your losses and move on Troll Boy.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com

Visit my Math Blog at http://www.dcproof.wordpress.com

[Eram semper recta]

Anonymous coward and king troll of sci.math Dan Christensen spammed:


> "There are no points on a line."

Lie. I never said that. What I did say is that a line does not consists of points. When we talk about points on a line, we really mean distances that are indicated much like road signs do for distances travelled along a road.

A line is one of innumerable distances between any two points.
A straight line is the shortest distance between two points.


> "Pi is NOT a number of ANY kind!"

True. Pi is merely a symbol for an incommensurable magnitude - apparently a concept too advanced for an imbecile like Dan Christensen.

> "1/2 not equal to 2/4"

Lie. I have NEVER said this. What I have talked about is the difference in the process of measure.

What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.

There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:

_ / _ _
_ _ / _ _ _ _

The length _ is not equal to the length _ _ .

> “1/3 does NOT mean 1 divided by 3 and never has meant that”

True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

Also, my article on pi not being a number of any kind:

https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3

The true story of how we got numbers:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

No such thing as a "real number" or a "real number line":

https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc

There is no valid construction of "real number" - it's a myth:

https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU

> "3 =< 4 is nonsense.”

True. In mathematics, it is called an invalid disjunction.

3 <= 4 means EITHER 3 < 4 OR 3 = 4

Actually, there is no "OR" part, so the logical disjunction is invalid.

> "Zero is not a number."

True. While not a number of any kind, it is very useful in mathematics.

https://drive.google.com/file/d/1w2tt7IgoIu-ychDCoYi-4jOAzToy0ViM

> "0 is not required at all in mathematics, just like negative numbers."

Half-truth. While negative numbers are not required in mathematics, they are extremely useful.

> “There is no such thing as an empty set.”

True. Even the father of all mainstream mathematical cranks rejected the idea of empty set. But let's not go too far ... there isn't even a definition of "set" in set theory!

https://youtu.be/KvxjOMW6Q9w

https://youtu.be/1CcSsOG0okg

> “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)

True. These are propositions that are implied by the given equations. For example, my historic geometric identity states:

[f(x+h)-f(x)]/h = dy/dx + Q(x,h)

And so, f(x+h)-f(x)]/h <=> dy/dx + Q(x,h)

The theorem:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

How it provides a rigorous definition of integral for the flawed mainstream calculus:

https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

The day will come when this vicious anonymous troll Dan Christensen is convicted in a court of law.

Download for free the most important mathematics book ever written:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view

The New Calculus is proof that you CAN DO calculus without the use of LIMIT THEORY.

Don't believe me? Study it. You will be pleasantly surprised.

I am a genius and the greatest mathematician alive today.

[zelos...@gmail.com]

I have refuted EVERYTHING and you just go "NU UH!"

[Eram semper recta]

You had better start coming up with something a lot more interesting than just trying to flatter me. Yes, I know imitation is thought to be the sincerest form of flattery, but I have never liked flattery. That is a narcissistic trait.

[zelos...@gmail.com]

You are a narcissist through and through

[Eram semper recta]

Opinions are a nickel a dozen. LMAO.

[zelos...@gmail.com]

That is why none cares about yours.

[Eram semper recta]

Another false opinion. Tsk, tsk. You never learn, do you Malum... Sigh.

Can anything get more cranky than claiming that "if c=f+g then g=c-f is circular" ? LMAO

You went along with that delusional psychopath Jean Pierre Messager (aka Python).

That is what YOU said! You are a crank! Here it is again with link following:

***************************************************************
> > He think that stuff you point out is circular
> >
> > if c=f+g
> > then g=c-f
> > so circular!
***************************************************************

https://groups.google.com/g/sci.math/c/QMhqLZH1434/m/vAEmniRtBwAJ

[markus...@gmail.com]

lördag 21 augusti 2021 kl. 14:12:07 UTC+2 skrev Eram semper recta:

Countable does not mean "systematically named" (which isn't really a thing to begin with). All sets can be "systematically named" by just naming every element.

[Eram semper recta]

It does, you idiot!

***A set is countable iff its members can be systematically named.***

This is why you can say that if any set S is in a bijection with |N or a subset of |N that S is countable, because |N itself can be systematically named! Why do you think Cantor chose |N as an index set? Ever think about this, you stupid moron?

> (which isn't really a thing to begin with).

What does a "thing" even mean? It's bullshit that only you know what you are babbling about.

> All sets can be "systematically named" by just naming every element.

Not quite! Systematically named does not just mean naming at random. It means naming in "order", ie, in an orderly way from one element to the next.

Now do you want to try again to name the "elements" of that bogus set you call "real numbers"? LMAO

[markus...@gmail.com]

Well, if you require ordering you can just consult the axiom of choice. :)
(of course this isn't a requirement)

[Eram semper recta]

Nope. The axiom of choice is a "belief" in the bullshit of set theory and not at all required to order the natural numbers.

Still waiting for you "valid systematic naming of that imaginary set called <real numbers>". Chuckle.

[Ross A. Finlayson]

That each real number has a name is Eudoxus/Dedekind/Cauchy,
their real numbers are the complete ordered field.

That there are models of real numbers like countable line reals,
I've written this up quite a bit.

Having a mathematics degree is at least some demonstrated
command of the fundamental derivations what result real analysis etc.

I have three definitions of continuity and Cantor's included
and proves the line is drawn.



One of the usual results in the linear curriculum is the uniqueness of
R as the complete ordered field up to isomorphism, but I wrote some
field operations for [-1,1]. (Non sequitur.)

[markus...@gmail.com]

That's not what the axiom of choice is use for, what?`

The existence of the natural numbers in set theory relies on the axiom of infinity. I wouldn't expect you to know the difference honestly, but they are not the same.

And my point still stands: All sets can be "systematically named" by just naming every element.

[Ross A. Finlayson]

On Saturday, August 28, 2021 at 8:24:11 AM UTC-7, markus...@gmail.com wrote:
> That's not what the axiom of choice is use for, what?`
>
> The existence of the natural numbers in set theory relies on the axiom of infinity. I wouldn't expect you to know the difference honestly, but they are not the same.
>
> And my point still stands: All sets can be "systematically named" by just naming every element.

Excuse me for interjecting for instead a comment that
the, existence of, a ground model, of finite ordinals,
in ZF, might be for its undecideability, that there are
only bounded fragments, and, extensions.

Sets are defined by their members it's true.


AC or Ono or Zorn's Lemma or the Well-Ordering principle,
Zermelo strongly included it or for its justification as being
"true", that, there are arbitrarily large ordinals and
functions are Cartesian in the space of their image.

(Where it is most usual in "set theory" to model "functions"
this way, for "set theory", "number theory", "function theory",
"geometry", ..., each in terms of the others.)

("Descriptive set theory", "topology", ..., usually in "only a
Cartesian function theory", that there aren't non-Cartesian
functions with respect to the ranges of their image.)

Having a countable model of reals only [0,1] and
only line-drawing and specifically non-Cartesian the function
and specifically not-a-real-function but limit-of-real-functions,
makes for well-ordering these reals in their natural order.

[New Age Prophet]

No idea what you are asking in the above question, but AOC is not even relevant in the discussion.

>
> The existence of the natural numbers in set theory relies on the axiom of infinity.

Absolute RUBBISH! Infinity is a 100% pure JUNK concept. Has no effect n natural numbers whatsoever. Now if you try to talk about an "infinite set", well then you are already lost because there is no such thing. Chuckle.

> I wouldn't expect you to know the difference honestly, but they are not the same.
>
> And my point still stands: All sets can be "systematically named" by just naming every element.

Your point is NO POINT at all. You've stated an empty claim.

Again crank, name those objects you call systematically for the interval (0,1) beginning with 0. LMAO.

[Ross A. Finlayson]

On Saturday, August 28, 2021 at 9:11:28 AM UTC-7, New Age Prophet wrote:


Hmm..., perhaps when it posting-limits itself, it _changes_ the account....

The trul.

[markus...@gmail.com]

Sure, an element in (0, 1) corresponds to choosing an integer valued function f:N to [0, 9]. The 'name' of an element in (0, 1) is simple the list of values f(1), f(2), f(3), ...

[Eram semper recta]

You'll get no more responses on this either because I simply cannot tolerate fools like you.

[markus...@gmail.com]

What would it take for you to realise learning math you do not know could potentially be a lot of fun? Try at least to understand bijections and cardinality before calling everyone else retards, vile Jews, morons, fools, apes and idiots.

[Eram semper recta]

> What would it take for me to realise learning math I do not know could potentially be a lot of fun?

Unfortunately, no matter what you do, you will ALWAYS be an incorrigible idiot who cannot be corrected.

> I should try to at least to understand bijections and cardinality

You really should, ballsack!

> Why do you call everyone else retards, vile Jews, morons, fools, apes and idiots.

But you and they are ALL of these things! I call you by YOUR names. Chuckle.

[zelos...@gmail.com]

I pointed out that is how YOU think. Not that I think it you dishonest lying sack of shit :)

[zelos...@gmail.com]

what you do not tolerate is people being more knowledgeable than you. Markus clearly knows mathematics better than you.

[zelos...@gmail.com]

Yet when people do that to you, you say they are guilty of "libel" and it is a weakness in their position cause they got nothing else.

There is a term for this. Hypocrisy. You're a hypocrite, Gerbil.

[Eram semper recta]

The lying sack of SHIT is YOU, you vile bastard.

I said the exact opposite of what you and Python were saying.

IF [f(x+h)-f(x)]/h = f'(x) + Q(x,h) THEN f'(x)= [f(x+h)-f(x)]/h - Q(x,h)

and then the two fucking morons (YOU and Python) tried to insinuate that it was circular. LMAO.

You're the world's greatest mainstream crank!

[zelos...@gmail.com]

You did when we discussed D and T, derivative and tangent, functions.

D was defined in terms of limit
T was defined in terms of D

yet you claim it was circular because D uses T after some re-arrangement. Just like the illustration I gave.

[Eram semper recta]

Lying again, crank? Nowhere did I say this. Provide the link, you vile bastard!

>
> D was defined in terms of limit

I have NEVER defined the derivative in terms of a limit. Newsflash: I do not use the bullshit of limit theory in my historic geometric theorem. It is 100% geometry:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

> T was defined in terms of D

That's EXACTLY what YOU do in your bullshit MAINSTREAM calculus and it is CIRCULAR.

>
> yet you claim it was circular because D uses T after some re-arrangement. Just like the illustration I gave.

Your drivel was nothing of the sort. You imagined that you were agreeing with your fellow asswipe Jean Pierre Messager (aka Python) and I made a fool of you yet again! LMAO.

[zelos...@gmail.com]

https://groups.google.com/g/sci.math/c/5NjpX0It60I/m/nLvlglEMCQAJ
https://groups.google.com/g/sci.math/c/bxHjnK8_00o/m/L5t27UkMCQAJ
https://groups.google.com/g/sci.math/c/QMhqLZH1434/m/a_ShbscMCQAJ
Right in this post :slight_smile:

>I have NEVER defined the derivative in terms of a limit.

I didn't say you did, I said I did. D was defiend in terms of limit, T in terms of D, and you cry circular which is not it.

To be circular T is defined in terms of D, and D in terms of T, but it isn't. D is defined independently of T

>That's EXACTLY what YOU do in your bullshit MAINSTREAM calculus and it is CIRCULAR.

See, right here you do claim it is circular just like I said you do.

D defined in terms of limit
T defined in terms of D
Is not circular. It is a linear progression of definitions.

>Your drivel was nothing of the sort. You imagined that you were agreeing with your fellow asswipe Jean Pierre Messager (aka Python) and I made a fool of you yet again! LMAO.

You didn't, you did however manage to confirm in this post exactly what I said you did while denying it. That is quite foolish.

[New Age Prophet]

On Saturday, August 21, 2021 at 8:12:07 AM UTC-4, Eram semper recta wrote:
> Cantor was right in saying that the mythical set of real numbers is uncountable, but not for the reasons he thought!
>
> The "set of real numbers" is uncountable because its members cannot be systematically listed. Most of the members don't even exist!
>
> Defn: A set is countable if its members can be systematically named.
>
> Other definitions:
>
> A set is countable if its members can be indexed.
> (This is similar to saying: A set is countable if its members can be placed into a bijection with |N or a subset of |N).
>
> Why is |N itself countable? Because the members of |N can be systematically NAMED using any radix system.
>
> A set is countable if its members can be systematically listed.
>
> Now Wolfgang Mueckeheim will talk about ALL the members but this is not what Cantor meant - even if Cantor did say ALL. Cantor was delusional but not so stupid as to mean ALL members.
>
> Cantor's DIAGONAL (mis) ARGUMENT is the joke of the 20th century. In it, Cantor assumes that every "real number" (no such thing!) has an "infinite decimal expansion" which is FALSE.
>
> However, if one accepts that every "real number" (no such thing!) has a mythical "infinite decimal expansion", then the set (0,1) can be systematically named as demonstrated in my video:
>
> https://youtu.be/hlqTuuhR3-4
>
> Since set (0,1) is equipollent to (-oo, oo), it follows that the set (-oo, oo) is therefore countable. Q.E.D.
>
> Mainstream mathematics academics are far too stupid to match my insight and depth of understanding. I am the greatest mathematician alive today. This is not a delusion, but a FACT.
>
> Yes, I do know better!

Essentially what the Baboons of mainstream academia will have you believe is that:

t(c+h)-t(c)]/h = Lim (h->0)[f(c+h)-f(c)]/h = f'(c) + Q(c,h) and is possible ONLY if Q(c,h)=0, but this happens only in the case of the straight line t(x). It NEVER happens with the finite difference quotients. The mainstream want you to believe that there is some finite difference ratio hovering at infinity which produces f'(c):

t(c+h)-t(c)]/h = [f(c+h_1)-f(c)]/h_1 ; [f(c+h_2)-f(c)]/h_2 ; [f(c+h_3)-f(c)]/h_3 ; ... ; [f(c+h_3n-f(c)]/h_n ...; [f(c+h_oo)-f(c)]/h_oo

t(c+h)-t(c)]/h = [f(c+h_oo)-f(c)]/h_oo ?! What?!!! There is no such finite difference. It does not exist! But Baboon mathematics of the mainstream insists there is a limit!

Can you imagine how embarrassed Newton and Leibniz would be at these idiots today?! They knew that they could not solve the tangent line problem - this had to wait for the great John Gabriel. It is I who revealed to the entire world that:

[f(x+h)-f(x)]/h = f'(x) + Q(x,h)

It usually takes a genius to realise the most simple concepts that escape the syphilitic brains of highly educated idiots in the mainstream.

[markus...@gmail.com]

h is never 0. Learn limits.

[Ross A. Finlayson]

On Wednesday, September 1, 2021 at 1:31:24 PM UTC-7, markus...@gmail.com wrote:
> h is never 0. Learn limits.

It's "non-standard" to suggest that an infinite sum exists that actually equals its limit.

Which is that it was most standard in basically the stroke, or, decision rule,
that allowed analysts before Weierstrass with delta-epsilonics as it were,
to arrive at "enough rigor that it's not let out to quantities the limit as
for that when limits don't meet they fail to define the existence of two-sided limits".

Yes, learn limits, and, indeed hew to them, and also allow for free analysis,
of course demanding what rigor coincides for usual deductive and analytical
results: for where that the limit is not different than the sum. (Of negative
quantities of a series what might result zero or that limit sinc = 0.)

Countable additivity is a key of set theory about analysis,
while, uncountable measurable sets, are topologically what
are so accordingly of non-zero and finite measure.

Here analysis is as after follows "delta-epsilonics", which of course includes limits,
and even as defines them.

I.e. a usual assortment of fundamental theorems are of course written in delta-epsilonics.

[Ross A. Finlayson]

which is a secondary offshoot of real number theory

Of course delta-epsilonics is required and no-one goes around telling people
"Dedekind cuts, made of rationals, make real numbers, and that is the analytical
character and without telling you that also you've defined its basis for signal
analysis instead, the 'signal analysis of the Dedekind cuts as a continuous domain
with measure 1.0 real character', no, evrything is delta-epsilonics and besides that
also supporting the usual field reals, and line real for that matter."

delta-epsilonics

Of course the signal domain of rational numbers or the real numbers,
makes for the usual the "frequency as of a time component" doubles
as it were the usual re-constructive: "which is a secondary offshoot
of real number theory".

[zelos...@gmail.com]

onsdag 1 september 2021 kl. 13:30:40 UTC+2 skrev New Age Prophet:

No one in mathematics states that. That is your idiocy

[Eram semper recta]

Of course it is never 0 nor can be!

> Learn limits.

You mean, learn the art of hand waving in mainstream mathematics? :)

My historic theorem tells you that Q(x,h) is a *CONSTANT* for any given non-parallel secant line. The limit of a constant is the constant itself. Your hand waving technique takes

[f(x+h)-f(x)]/h = f'(x) + Q(x,h) [HGID]

and attempts to disguise it as

[f(x+h)-f(x)]/h = f'(x) + Lim_{h->0} Q(x,h)

Now Lim_{h->0}Q(x,h) = 0

But if you put Q(x,h)=0 in [HGID], then the identity no longer holds meaning the theorem cannot be true, but as we know, theorems are by definition true.

LMAO. You've been given ample examples and all you've done so far is reveal to the world what a true nincompoop you are.

[markus...@gmail.com]

As said above, h is never 0. We take a limit, as h approaches 0. It's not actually 0.

[zelos...@gmail.com]

torsdag 2 september 2021 kl. 12:07:18 UTC+2 skrev Eram semper recta:

You equate "I, John Gabriel, do not understand it" with "hand waving"

[Eram semper recta]

cr
What YOU say is irrelevant. What matters is what I tell you. h or Q(x,h) is only 0 when f is a straight line. At all other times, h is greater than 0 and has to be so for each of the UNIQUE tangent lines. h doesn't move as you think it does in your bogus Newtonian calculus. Chuckle. h is a CONSTANT for any given non-parallel secant line. Tell me moron, do you even bother trying to understand what I tell you? Just ask nicely and I'll help you. I am the greatest mathematician alive today.

> We take a limit, as h approaches 0. It's not actually 0.

The idiots who came before you created a hand waving argument because taking a limit is EXACTLY equivalent to setting h=0 and then you are also destroying the identity [f(x+h)-f(x)]/h = f'(x) + Q(x,h) because then, you are saying Lim {h->0} [f(x+h)-f(x)]/h = f'(x) which is utter BULLSHIT for the many reasons explained.

https://drive.google.com/file/d/1peL7lzXsmZ4AVsgAwDLvn8QIZbWy8Ebm

If you remove the link from your response, I shall stop teaching you!!

[markus...@gmail.com]

Why does it matter that no secant line is the tangent line? The tangent line is defined by a limiting process.

You are not the greatest mathematician alive, because you are no mathematician at all. You are a guy with "theories".

[Eram semper recta]

Because no secant line ever has the same slope as the tangent line.

> The tangent line is defined by a limiting process.

Rubbish. Rather the "limiting process" (aka hand waving argument) is defined by the non-parallel secant line slopes approximating the tangent line slope more closely. The method shows the failure of Newton and Leibniz in solving the tangent line problem.

>
> You are not the greatest mathematician alive, because you are no mathematician at all. You are a guy with "theories".

I piss and shit on what you think. When will you learn, idiot?

[zelos...@gmail.com]

when will you learn basic mathematics?

[markus...@gmail.com]

The "tangent line" isn't some magical thing that exists independent without limits. The tangent line is *per definition* defined by using a limiting process.

[Python]

markus...@gmail.com wrote:
...

> The "tangent line" isn't some magical thing that exists independent without limits. The tangent line is *per definition* defined by using a limiting process.

Exactly. John is doing exactly the same mistake in his idiotic "new
calculus" and in his stupid attempt to "fix" real calculus by removing
limits. In both cases at *no point* he is actually using the property
of being a tangent line. All his claims are hopeless and void and lead
to absolutely *nothing* relevant to the slopes of the tangent lines.

[Ross A. Finlayson]

It's not like the simple employ of quadratic antiquarature what
makes for simple simulated methods for the computation of
solutions in finite fields.

That's not to say that something like "the prime numbers are
simple about the quadratic sieve in terms of factoring algorithms"
or "the Galois field and various elliptical fields have various methods
what provide all sorts of integer solution in simple mathematics of
the quadratic" isn't a great thing, but, clearly it's just a little tool and
not the underlying geometry itself: just some mathematical leverage.

I.e., it's not like tomorrow he's going to make cryptography as usual
quite obsolete or as usually.

[Eram semper recta]

Of course it does, moron! There was not even a notion of "limit" over 2000 years ago.

> The tangent line is *per definition* defined by using a limiting process.

By the buffoons in mainstream academia. Their opinion, like yours is irrelevant. Stupid people do not get to define anything.

[Eram semper recta]

On Monday, 6 September 2021 at 18:24:07 UTC+3, Psychopath Jean Pierre Messager aka YBM aka JPM aka Python wrote:
> markus...@gmail.com wrote:
> ...
> > The "tangent line" isn't some magical thing that exists independent without limits. The tangent line is *per definition* defined by using a limiting process.

> Exactly. John is doing exactly the same mistake in his idiotic "new
> calculus" and in his stupid attempt to "fix" real calculus by removing
> limits.

There are no "limits" in Newton's or Leibniz's calculus.
Too bad for you, but my historic geometric theorem does exactly this - removes the bullshit of limits from calculus once and for all. It does more than this, it exposes what buffoons are you and others of your persuasion.

<drivel >

What happened to the "student projects" you promised would be forthcoming in January 2020? Chuckle.

[markus...@gmail.com]

It's not an opinion, it's just how the standard definition goes. Open any undergrad textbook in real analysis and this is the definition of the tangent line you will see.

There is no tangent line without limits.

[Python]

Ross, please could you refrain posting complete unrelated nonsense?

You're making a fool of yourself for no reason.

Thank you.

[Python]

Crank John Gabriel, aka Eram semper recta wrote:
...

>> Exactly. John is doing exactly the same mistake in his idiotic "new
>> calculus" and in his stupid attempt to "fix" real calculus by removing
>> limits.
>
> There are no "limits" in Newton's or Leibniz's calculus.

> Too bad for you, but my historic geometric theorem ...

you have no "theorem", you're an idiot and a psychopath.

>> In both cases at *no point* he is actually using the property
>> of being a tangent line. All his claims are hopeless and void and lead
>> to absolutely *nothing* relevant to the slopes of the tangent lines.

This hurts you because you know that it is true, John.

[Ross A. Finlayson]

Oh, so now who broke RSA.

And elliptical fields, ....

No, I only wrote plain sense, clearly though just a hint not some
"usual algorithm implemented in silicon, electronically, or on-paper",
what the mechanics of congruence work out and down.

Thank you, though, thank you usually, but, it'd be more appreciated
that _you_, _you_ post less non-sense, regardless its target or origin.

Then of couse also otherwise usually I'm the authority. (For what I care.)

8192 y u no 32-bit?

For, I know _you_ can post much "less non-sense", about anything _intresting_,
what mathematics is interesting and we all know it.

That for mathematics then please humbly accept my apology and contriteness,
what I will be the same way.

Indeed you should look down the hall and notice the office.

No, thank you, quadratic factoring and powers is of course of great interest,
that in a usual course of mathematics is part its own _field_.

This would probably usually be after concrete mathematics.

[Serg io]

On 9/1/2021 6:30 AM, New Age Prophet wrote:
> On Saturday, August 21, 2021 at 8:12:07 AM UTC-4, Eram semper recta wrote:
>> Cantor was right in saying that the mythical set of real numbers is uncountable, but not for the reasons he thought!
>>
>> The "set of real numbers" is uncountable because its members cannot be systematically listed. Most of the members don't even exist!
>>
>> Defn: A set is countable if its members can be systematically named.
>>
>> Other definitions:
>>
>> A set is countable if its members can be indexed.
>> (This is similar to saying: A set is countable if its members can be placed into a bijection with |N or a subset of |N).
>>
>> Why is |N itself countable? Because the members of |N can be systematically NAMED using any radix system.
>>
>> A set is countable if its members can be systematically listed.
>>
>> Now Wolfgang Mueckeheim will talk about ALL the members but this is not what Cantor meant - even if Cantor did say ALL. Cantor was delusional but not so stupid as to mean ALL members.
>>
>> Cantor's DIAGONAL (mis) ARGUMENT is the joke of the 20th century. In it, Cantor assumes that every "real number" (no such thing!) has an "infinite decimal expansion" which is FALSE.
>>
>> However, if one accepts that every "real number" (no such thing!) has a mythical "infinite decimal expansion", then the set (0,1) can be systematically named as demonstrated in my video:
>>
>> https://youtu.be/hlqTuuhR3-4
>>
>> Since set (0,1) is equipollent to (-oo, oo), it follows that the set (-oo, oo) is therefore countable. Q.E.D.
>>
>> Mainstream mathematics academics are far too stupid to match my insight and depth of understanding. I am the greatest mathematician alive today. This is not a delusion, but a FACT.
>>
>> Yes, I do know better!
>

> Essentially what the Baboons *INSULT* of mainstream academia will have you believe is that:
>
> t(c+h)-t(c)]/h = Lim (h->0)[f(c+h)-f(c)]/h = f'(c) + Q(c,h) *QUACK* and is possible ONLY if Q(c,h)=0 *QUACK* , but this happens only in the case of the straight line t(x). It NEVER happens with the finite difference quotients. The mainstream want you to believe that there is some finite difference ratio hovering at infinity which produces f'(c):

>
> t(c+h)-t(c)]/h = [f(c+h_1)-f(c)]/h_1 ; [f(c+h_2)-f(c)]/h_2 ; [f(c+h_3)-f(c)]/h_3 ; ... ; [f(c+h_3n-f(c)]/h_n ...; [f(c+h_oo)-f(c)]/h_oo
>

> t(c+h)-t(c)]/h = [f(c+h_oo)-f(c)]/h_oo ?! What?!!! There is no such finite difference. It does not exist! But Baboon *INSULT* mathematics of the mainstream insists there is a limit!
>
> Can you imagine how embarrassed Newton and Leibniz would be at these idiots *INSULT* today?! They knew that they could not solve the tangent line problem - this had to wait for the great John *QUACK* Gabriel. It is I who revealed to the entire world that:
>
> [f(x+h)-f(x)]/h = f'(x) + Q(x,h) *QUACK*
>
> It usually takes a genius to realise the most simple concepts that escape the syphilitic *INSULT* brains *INSULT* of highly educated idiots *INSULT* in the mainstream.
>

[Eram semper recta]

It is an opinion. You can fool others, but when you fool yourself, this means you stop learning.

> Open any undergrad textbook in real analysis and this is the definition of the tangent line you will see.

I've already told you: just because something is written in a book - textbook or otherwise, does not mean it is a fact.

So you are "Nah Uhing" me here again?

>
> There is no tangent line without limits.

You're delusional. Over 2500 years ago, the Ancient Greeks defined the tangent line for the very reasons I explained to you. There was not even a hint of the hand waving bullshit of limits back then.

Learn from me, idiot! The tangent line concept was realised as a means of measuring the SMOOTHNESS of curves. Yes, my brilliant ancestors were already thinking these things while yours were still busy splitting your heads with axes.

[zelos...@gmail.com]

>It is an opinion. You can fool others, but when you fool yourself, this means you stop learning.

Yours is just your opinion so what are you going to do about it? You are in no better position no matter how much you want to cry about it.

>I've already told you: just because something is written in a book - textbook or otherwise, does not mean it is a fact.

This includes Euclides books, because it says it doesn't that make it a fact and you stating it doesn't make it a fact.

The fact is however that normal university course literature do state the standard definitions that mathematics uses and you cannot argue against mainstream mathematics without using and understanding them.

>You're delusional. Over 2500 years ago, the Ancient Greeks defined the tangent line for the very reasons I explained to you. There was not even a hint of the hand waving bullshit of limits back then.

There is no handwaving and again, because it is in Euclids book doesn't that mean it is a fact :)

>Learn from me, idiot! The tangent line concept was realised as a means of measuring the SMOOTHNESS of curves. Yes, my brilliant ancestors were already thinking these things while yours were still busy splitting your heads with axes.

Not what smoothness means in mathematics.

[Eram semper recta]

On Tuesday, 7 September 2021 at 11:15:51 UTC+3, zelos...@gmail.com wrote:

<not worth response>

> There is no handwaving and again, because it is in Euclids book doesn't that mean it is a fact :)

If it's in the Elements, it is most definitely and unquestionably a FACT!

See, this proves you are a crank! LMAO.

A Malum is one who cannot be convinced in the face of overwhelming evidence.

Henceforth, Malum and Crank are two different words with the same meaning. LMAO.

[zelos...@gmail.com]

>If it's in the Elements, it is most definitely and unquestionably a FACT!

>I've already told you: just because something is written in a book - textbook or otherwise, does not mean it is a fact.

You already said that because it is in a book doesn't that mean it is a fact. That applies to Euclides as well.

>See, this proves you are a crank! LMAO.

What, pointing out your own hypocrisy? That when it is books you don't like it doesn't count but when it is books you like it counts?

That is cherry picking and hypocrisy.

[markus...@gmail.com]

Apart from you simply misunderstanding smoothness, common definitions are seen as standard because everyone else is using them. Math isn't "true" or "false" because it's in a textbook, but terminology can be standard or non-standard depending on its usage in textbooks.

The standard definition of the tangent line uses limits, so this is what the definition means to 99% of people.

[Eram semper recta]

On Tuesday, 7 September 2021 at 14:42:28 UTC+3, zelos...@gmail.com wrote:
> >If it's in the Elements, it is most definitely and unquestionably a FACT!
> >I've already told you: just because something is written in a book - textbook or otherwise, does not mean it is a fact.
> You already said that because it is in a book doesn't that mean it is a fact. That applies to Euclides as well.

No, it does not apply to Euclid. Fools who came after the Ancient Greeks are not in the same league. Chuckle.

The Elements have withstood the test of time. Your bullshit mainstream mythmatics is about to be dismantled by me. LMAO.

[Eram semper recta]

> Apart from you simply misunderstanding smoothness, common definitions are seen as standard because everyone else is using them. Math isn't "true" or "false" ...<drivel>

Math is either right (true) or wrong (false). Nothing else.

[markus...@gmail.com]

Conventions and definitions aren't: they are decided upon collectively.

[New Age Prophet]

I piss an shit on conventions. There was no baboon council over 2300 years ago when mathematics was first realised by my ancestors. The Elements has endured because of its well-formed definitions.

> they are decided upon collectively.

No. Mathematics is NEVER done by consensus. Imagine a bunch of apes like you being in control. Sheeesh, what a nightmare!

[markus...@gmail.com]

Of course you "piss an shit" on conventions. That's what I'm saying. You are making up your non-standard definitions to words already well-established and well-used. Deceiving at best, ignorant at worst. Choose.

[Dan Christensen]

STUDENTS BEWARE: Don't be a victim of JG's fake math

That explains in part why you, Troll Boy, are unable to derive even the most elementary results of basic arithmetic, e.g. that 2+2=4, in your goofy little system. Your conventions/definitions simply don't work.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

[Uwus Semmelmagus]

> Fools who came after the Ancient Greeks are not in the same league. Chuckle.

Hello Eram,
what is your opinion on the Basileia Rhomaion?
Best,
Uwus

[zelos...@gmail.com]

This is called special pleading
https://en.wikipedia.org/wiki/Special_pleading

You make a rule then the one you want is suddenly excempt.

It is just a book and you say because it is in a book doesn't that mean it is a fact.

And today, it is insufficient and has been for centuries.

[markus...@gmail.com]

And at the same time, he can't rigorously define his own definitions.

[Eram semper recta]

YOUR "conventions" are nothing but garbage. Mathematics is not based on convention, only hard cold facts and reason.

When you sacrifice to Odin, that is what is called convention. Chuckle.

> That's what I'm saying.

Over 99% of the time, you have no clue what you are saying.

> You are making up your non-standard definitions to words already well-established and well-used.

LIE. I am the one directing you to the object of your loathing - the dictionary. You hate this because it exposes your ignorance.

> Deceiving at best, ignorant at worst. Choose.

In your case, both ignorant and deceitful.

[zelos...@gmail.com]

>only hard cold facts and reason.

What you mean here is your opinion.

>LIE. I am the one directing you to the object of your loathing - the dictionary.

The dictionary does not define what words mean in mathematics. The mathematics textbooks do.

And again, Euclid's Elements is just a book, it is no more special than any other mathematical book. It is severely outdated today and insufficient by modern needs.

[markus...@gmail.com]

Yeah, but you can't disprove math by a dictionary. AS numerous people already have pointed out.

[Eram semper recta]

Straw man argument again. Don't you ever tire of LYING?

[markus...@gmail.com]

What...? How is pointing out you cannot debate mathematics itself with a dictionary a strawman?

[Eram semper recta]

Boy, you are dumber than I thought. Your name is STRAW MAN.

I never debated mathematics using any dictionary. What I have been showing you is your inability to communicate and to provide any rational argument, because for starters you do not understand the meaning of most words that you use. The meaning of such words comes from a dictionary. You go on about conventions and all that crap, but the dictionary is the starting point and a convention for the way words are used. You cannot change the meaning of words in a dictionary because then what you'll have is utter chaos.

All this will go right past you no doubt!

[markus...@gmail.com]

Meaning of words comes from their usage, not a dictionary. A dictionary doesn't usually contain technical uses, so you're just wrong here again it seems.

[Eram semper recta]

On Saturday, 21 August 2021 at 15:12:07 UTC+3, Eram semper recta wrote:
> Cantor was right in saying that the mythical set of real numbers is uncountable, but not for the reasons he thought!
>
> The "set of real numbers" is uncountable because its members cannot be systematically listed. Most of the members don't even exist!
>
> Defn: A set is countable if its members can be systematically named.
>
> Other definitions:
>
> A set is countable if its members can be indexed.
> (This is similar to saying: A set is countable if its members can be placed into a bijection with |N or a subset of |N).
>
> Why is |N itself countable? Because the members of |N can be systematically NAMED using any radix system.
>
> A set is countable if its members can be systematically listed.
>
> Now Wolfgang Mueckeheim will talk about ALL the members but this is not what Cantor meant - even if Cantor did say ALL. Cantor was delusional but not so stupid as to mean ALL members.
>
> Cantor's DIAGONAL (mis) ARGUMENT is the joke of the 20th century. In it, Cantor assumes that every "real number" (no such thing!) has an "infinite decimal expansion" which is FALSE.
>
> However, if one accepts that every "real number" (no such thing!) has a mythical "infinite decimal expansion", then the set (0,1) can be systematically named as demonstrated in my video:
>
> https://youtu.be/hlqTuuhR3-4
>
> Since set (0,1) is equipollent to (-oo, oo), it follows that the set (-oo, oo) is therefore countable. Q.E.D.
>
> Mainstream mathematics academics are far too stupid to match my insight and depth of understanding. I am the greatest mathematician alive today. This is not a delusion, but a FACT.
>
> Yes, I do know better!

Cantor cranks are worse than Islamic fundamentalists.

[markus...@gmail.com]

That's not the definition. Strawmanning again.

[zelos...@gmail.com]

söndag 12 september 2021 kl. 14:44:07 UTC+2 skrev Eram semper recta:

This comes from the one constantly saying there is ONLY ONE WAY.

Goes only from ONE BOOK that is INFALLIBLE and ALWAYS correct...just like fundamentalists do.

[Eram semper recta]

It is very much the definition.

[zelos...@gmail.com]

All of it is wrong. |(0,1)|>|N| so R is not countable.

The diagonal argument with decimal expansions, again we can have infinite, is one that is easy for people to understand. You can argue from constructions instead and show without focusing on representations that |R|>|N|

[markus...@gmail.com]

Correction: it's your definition, a definition no one uses and not what any other human would mean. Also it doesn't mean anything. Any set can have its members indexed by itself..

[Eram semper recta]

Well, it's not my definition because it is well-known what my opinion is on most of Dedekind's bullshit theories. Cuts are not a valid construction of real number as I proved in my fine article. What any other human would mean is neither here nor there. Those few who are intelligent know I am correct. Where Trump supporters like you are concerned, all bets are off. LMAO

> Also it doesn't mean anything.

FALSE. A well-formed definition means everything.

> Any set can have its members indexed by itself.

Rubbish. Members of a set must be distinct. So far, your Chambers university degree hasn't helped you one bit in understanding these things. The only sets that can be used as indexes are |N and |Q. There is no set of "real numbers". Chuckle.

[zelos...@gmail.com]

>Well, it's not my definition because it is well-known what my opinion is on most of Dedekind's bullshit theories.

It is known what you think and it is equally well known you do not understand how dedekinds cuts work because you cannot even do them right!

>Cuts are not a valid construction of real number as I proved in my fine article

You proved nothing of the sort because none of your finite sets are dedekinds cuts. NO finite set can be!

>Those few who are intelligent know I am correct.

Any intelligent person can read the definition of a dedekind cut and know no finite set will ever be it!

[Greg Cunt]

On Saturday, August 21, 2021 at 2:12:07 PM UTC+2, Eram semper recta wrote:

> every real number [...] has an [...] decimal expansion

Right!

> Since set (0,1) is equipollent to (-oo, oo), it follows that the set (-oo, oo) is [un]countable.

Exactly!

See: https://en.wikipedia.org/wiki/Uncountable_set

[markus...@gmail.com]

I can index a set by the real numbers.

R={r_i: i \in R and r_i \in R}.

Also none of those sets are cuts so everything you say is invalid.

[Eram semper recta]

In your dreams, you silly boy! In order to do this, you would have to be able to systematically name the elements of your imaginary set R. LMAO at how fucking stupid you are! Chambers university? Just to think, they have produced many idiots like you!

>
> R={r_i: i \in R and r_i \in R}.

Man, you just nailed yourself on this one also! What the fuck is r_i ? If you mean the subscript "i" is an index, then you have admitted your imaginary R is <<countable>> but too stupid to have noticed it. LMAO.

<drivel>

[markus...@gmail.com]

Index sets doesn't have to be countable. r_i is an element of R with index i, and the index is a real number. You can index any set with itself.

[zelos...@gmail.com]

Read up on index sets mate, I have linked you before and you still get it wrong.

[Eram semper recta]

An index set has to be countable, otherwise it can't be used as an index.

To be countable, a set must have elements that can be systematically named.

As for Cantor's bijective cardinality between continuous "sets" such as (0,1) and (-oo,oo), this is just nonsense because mapping distances to flags is meaningless if said distances cannot be measured. The poor insane Cantor's discovery of scaling proves nothing about bijection. That __ can be scaled to double its size ____ was known thousands of years ago and does not mean that __ and ____ are equipollent. You can assign any number of flags to either __ or ____, but there is no one to one correspondence between the distances - most of which have no measure.

Cantor was the father of all mainstream math cranks:

https://youtu.be/HYLkDZ0BdAk

Flags DO NOT imply equinumerosity:

https://youtu.be/PfLS9ySOqHs

> r_i is an element of R with index i,

And this folks, is why I would never allow idiots to produce definitions for consideration.

<PLONK>

> and the index is a real number.

There is no such thing as a "real number".

> You can index any set with itself.

In which case your mythical set of "real numbers" is countable.

[markus...@gmail.com]

No, a index set doesn't have to be countable and for you I would imagine you only accept finite index sets anyway.

[zelos...@gmail.com]

There is nothing that says an index set must be countable.

[Eram semper recta]

An index set MUST be countable, meaning that its members can be systematically NAMED or LISTED.

You've NEVER understood what Cantor meant by "countable set" - not even Prof. Wolfgang Mueckenheim understands.

You were taught to determine set countability by verifying whether its elements could be placed into a one-to-one bijection with |N. You couldn't do this if the elements of |N are not distinct and therefore NAMED (as in a radix representation).

Klyver, you are a clown. When you started out studying my work you were on the right track, then your orangutan lecturers poisoned your brain and now you are in a downward spiral as they have turned you into twice the morons they are.