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Why No Irrationals exist, and why pi and 2.71… are rational numbers-- as easy as Decimal Number representation-- they have a denominator power of 10
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Archimedes Plutonium
Oct 14, 2017, 9:09:06 PM10/14/17
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Why No Irrationals exist, and why pi and 2.71… are rational numbers
Old Math, and their "Lowest Terms Error" although don't tell them-- proved that 1/2 is irrational Re: analyzing why the Ancient Greek proof that sqrt2 is irrational is flawed
Alright, let me get started on the proof that 1/2 is irrational number using the invalid method of Ancient Greeks that sqrt2 is irrational, only because, the method is invalid.
Earlier I showed how a definition of Lowest Term for p/q needed to be extended to include a number in Rationals in decimal representation. So, what is the Lowest Term for 1/2 in 10 Grid, for it would be .1/.2 and then the next lowest is .2/.4, etc etc.
So, let us run through a proof that 1/2 is a Irrational number using the proof method of Ancient Greeks.
Proof:: Suppose 1/2 is Rational. And now, put 1/2 in Lowest terms and it is thus, in lowest terms. But now, taking 2 and dividing it into 1
__________
2| 1.00000.... = .50000.....
and then dividing 2 by 2
_________
2|2.00000..... = 1.0000.....
And now, we have 1/2 in Lowest terms as .5/1.
But now, hold on a minute, let us divide .5 by 2, then 1 by 2, giving us .25 and .5 respectively.
Since we can never get a Lowest Term for the Rational number 1/2, means a contradiction, hence 1/2 is irrational.
So, of course the above is flawed and flawed in the same way the method was used to prove sqrt2 is irrational, when truly sqrt2 is rational.
What went wrong? What went wrong is a bad definition-- Lowest Terms.
The proof that sqrt2 is Rational, simply involves observation for that
In 10 Grid, sqrt2 = 1.42 X 1.42 = 2.0 (oh, you question the 2.0164, you question the "164", well in 10 Grid, the only digits that exist are the ten place value and that is 2.0.
In 100 Grid, sqrt2 = 1.415 X 1.415
In 1000 Grid, sqrt2 = 1.4143 X 1.4143 and on and on.
Sqrt2 and all sqrt root numbers are Rationals. Even pi and 2.71.... are rational numbers.
AP
Anthyphairesis Re: Stillwell gave another phony proof sqrt2 irrational Re: analyzing why the Ancient Greek proof that sqrt2 is irrational is a flawed
On Sunday, October 8, 2017 at 6:06:01 PM UTC-5, Archimedes Plutonium wrote:
> On Sunday, October 8, 2017 at 3:50:43 PM UTC-5, Archimedes Plutonium wrote:
>
> >
> > That is the only one proof in all of mathematics-- an argument based on a definition of Lowest Terms.
>
> Apparently there is a second proof of sqrt2 irrational. A far more challenging proof to see if phony.
>
Apparently there was a second proof, but whether it was known by Euclid, by Archimedes, I rather doubt it.
> It is seen in Stillwell's Mathematics and Its History, 3rd ed. 2010, page 45. In the same book, page 12 is the Lowest Terms phony proof.
>
> Now looking at that alleged proof on page 45, it says and I quote.
>
> " We notice that the rectangle remaining after step 2, with sides sqrt2-1 and 2-sqrt2 = sqrt2(sqrt2-1), is the same shape as the original, though the long side is now vertical instead of horizontal. It follows that similar steps will recur forever, which is another proof that sqrt2 is irrational, incidentally."
>
> Does Stillwell expect readers to "read his mind". Why would a recurrence ever make Stillwell think that was a proof of sqrt2 is not able to be P/Q where P and Q are Counting Numbers. Why? Is it because two rational sides would cancel out in a square further down the line? And, if so, then the reason this proof is nonrecurring is only because, well, you use a symbol of sqrt2 that cannot commingle with actual numbers. If you call a number a symbol, call it S, call it Y, obviously you cannot get rid of it.
>
> Now this one is going to be challenging for me to show it is phony. But it is easy if we demand sqrt2 be written as a number, not some abstract symbol. Once we demand that a number in decimal representation or in fractions be forced upon rather than a "just a symbol sqrt2", then the phoniness of the proof is immediately apparent. Because, that forcing demands sqrt2 be written as 1.42 = 142/100 in 10 Grid or written as 1.415 = 1415/1000 in 100 Grid, etc. Writing sqrt2 in a number, then it behaves like all other Rationals, for it is a rational.
>
> You see, the rub on sqrt2 that Old Math installed is the same mistake they made with 1/3. They want 1/3 be .33333....., when, if called to be logical, 1/3 is .3333...33(+1/3) what Newton called the Compleat Quotient.
>
nice proof that no irrationals exist, simple fact that all numbers are Decimal represented and thus a denominator of power of 10 Re: analyzing why the Ancient Greek proof that sqrt2 is irrational is a flawed
Now, here is a Commonsense proof that No Irrationals exist. It is not formal, it is not flowery or pilfered with abstractions. It is a proof that an old grandma or grandpa would understand and recognize, even if starting to slow to think in old age. It is a proof that young kids would be proud of owning. For it is a proof that since 3000 years ago, humanity has thought there was something known as "irrational number" and only now, today, realizes that there are no irrational numbers. That irrational numbers was the grand fake of fakeries.
Theorem Statement:: Rational numbers exist, but Irrationals do not exist.
Proof Statement:: Once we are able to have a Decimal Number system we can build all the numbers via Grids and using a math-induction element and adding that element successively to build the numbers. They are all Decimal numbers, meaning that their place-value is established. So that say for instance .003, or 3.14159..... are all rational numbers because, depending on what place value you want to talk about, it is 3/1000 or 314159/100000. In other words, writing a number in Decimal Representation alone, proves the number is a Rational for the denominator is always a power of 10. And since decimal numbers is ALL POSSIBLE DIGIT ARRANGEMENTS, means that all numbers are a Rational. QED
Now, there is one possible exception to this rule or proof. The imaginary number of square root of -1.
Is it even a number? I am going to say it is not a number, because all numbers have to come from Math induction on a induction element, be it 1 for Counting Numbers, be it .1 for 10 Grid, or .01 for 100 Grid, etc etc. So where does that leave us with sqrt -1. I suggest that i is not a number but an angle, a symbol for an angle. What angle is it? Not 90 degree for that is +1. I suggest i = sqrt-1 is the angle 180 degrees that lies in 2nd and 3rd quadrants.
Old Math, and their "Lowest Terms Error" although don't tell them-- proved that 1/2 is irrational Re: analyzing why the Ancient Greek proof that sqrt2 is irrational is flawed
Alright, let me get started on the proof that 1/2 is irrational number using the invalid method of Ancient Greeks that sqrt2 is irrational, only because, the method is invalid.
Earlier I showed how a definition of Lowest Term for p/q needed to be extended to include a number in Rationals in decimal representation. So, what is the Lowest Term for 1/2 in 10 Grid, for it would be .1/.2 and then the next lowest is .2/.4, etc etc.
So, let us run through a proof that 1/2 is a Irrational number using the proof method of Ancient Greeks.
Proof:: Suppose 1/2 is Rational. And now, put 1/2 in Lowest terms and it is thus, in lowest terms. But now, taking 2 and dividing it into 1
__________
2| 1.00000.... = .50000.....
and then dividing 2 by 2
_________
2|2.00000..... = 1.0000.....
And now, we have 1/2 in Lowest terms as .5/1.
But now, hold on a minute, let us divide .5 by 2, then 1 by 2, giving us .25 and .5 respectively.
Since we can never get a Lowest Term for the Rational number 1/2, means a contradiction, hence 1/2 is irrational.
So, of course the above is flawed and flawed in the same way the method was used to prove sqrt2 is irrational, when truly sqrt2 is rational.
What went wrong? What went wrong is a bad definition-- Lowest Terms.
The proof that sqrt2 is Rational, simply involves observation for that
In 10 Grid, sqrt2 = 1.42 X 1.42 = 2.0 (oh, you question the 2.0164, you question the "164", well in 10 Grid, the only digits that exist are the ten place value and that is 2.0.
In 100 Grid, sqrt2 = 1.415 X 1.415
In 1000 Grid, sqrt2 = 1.4143 X 1.4143 and on and on.
Sqrt2 and all sqrt root numbers are Rationals. Even pi and 2.71.... are rational numbers.
AP
Anthyphairesis Re: Stillwell gave another phony proof sqrt2 irrational Re: analyzing why the Ancient Greek proof that sqrt2 is irrational is a flawed
On Sunday, October 8, 2017 at 6:06:01 PM UTC-5, Archimedes Plutonium wrote:
> On Sunday, October 8, 2017 at 3:50:43 PM UTC-5, Archimedes Plutonium wrote:
>
> >
> > That is the only one proof in all of mathematics-- an argument based on a definition of Lowest Terms.
>
> Apparently there is a second proof of sqrt2 irrational. A far more challenging proof to see if phony.
>
Apparently there was a second proof, but whether it was known by Euclid, by Archimedes, I rather doubt it.
> It is seen in Stillwell's Mathematics and Its History, 3rd ed. 2010, page 45. In the same book, page 12 is the Lowest Terms phony proof.
>
> Now looking at that alleged proof on page 45, it says and I quote.
>
> " We notice that the rectangle remaining after step 2, with sides sqrt2-1 and 2-sqrt2 = sqrt2(sqrt2-1), is the same shape as the original, though the long side is now vertical instead of horizontal. It follows that similar steps will recur forever, which is another proof that sqrt2 is irrational, incidentally."
>
> Does Stillwell expect readers to "read his mind". Why would a recurrence ever make Stillwell think that was a proof of sqrt2 is not able to be P/Q where P and Q are Counting Numbers. Why? Is it because two rational sides would cancel out in a square further down the line? And, if so, then the reason this proof is nonrecurring is only because, well, you use a symbol of sqrt2 that cannot commingle with actual numbers. If you call a number a symbol, call it S, call it Y, obviously you cannot get rid of it.
>
> Now this one is going to be challenging for me to show it is phony. But it is easy if we demand sqrt2 be written as a number, not some abstract symbol. Once we demand that a number in decimal representation or in fractions be forced upon rather than a "just a symbol sqrt2", then the phoniness of the proof is immediately apparent. Because, that forcing demands sqrt2 be written as 1.42 = 142/100 in 10 Grid or written as 1.415 = 1415/1000 in 100 Grid, etc. Writing sqrt2 in a number, then it behaves like all other Rationals, for it is a rational.
>
> You see, the rub on sqrt2 that Old Math installed is the same mistake they made with 1/3. They want 1/3 be .33333....., when, if called to be logical, 1/3 is .3333...33(+1/3) what Newton called the Compleat Quotient.
>
nice proof that no irrationals exist, simple fact that all numbers are Decimal represented and thus a denominator of power of 10 Re: analyzing why the Ancient Greek proof that sqrt2 is irrational is a flawed
Now, here is a Commonsense proof that No Irrationals exist. It is not formal, it is not flowery or pilfered with abstractions. It is a proof that an old grandma or grandpa would understand and recognize, even if starting to slow to think in old age. It is a proof that young kids would be proud of owning. For it is a proof that since 3000 years ago, humanity has thought there was something known as "irrational number" and only now, today, realizes that there are no irrational numbers. That irrational numbers was the grand fake of fakeries.
Theorem Statement:: Rational numbers exist, but Irrationals do not exist.
Proof Statement:: Once we are able to have a Decimal Number system we can build all the numbers via Grids and using a math-induction element and adding that element successively to build the numbers. They are all Decimal numbers, meaning that their place-value is established. So that say for instance .003, or 3.14159..... are all rational numbers because, depending on what place value you want to talk about, it is 3/1000 or 314159/100000. In other words, writing a number in Decimal Representation alone, proves the number is a Rational for the denominator is always a power of 10. And since decimal numbers is ALL POSSIBLE DIGIT ARRANGEMENTS, means that all numbers are a Rational. QED
Now, there is one possible exception to this rule or proof. The imaginary number of square root of -1.
Is it even a number? I am going to say it is not a number, because all numbers have to come from Math induction on a induction element, be it 1 for Counting Numbers, be it .1 for 10 Grid, or .01 for 100 Grid, etc etc. So where does that leave us with sqrt -1. I suggest that i is not a number but an angle, a symbol for an angle. What angle is it? Not 90 degree for that is +1. I suggest i = sqrt-1 is the angle 180 degrees that lies in 2nd and 3rd quadrants.
Dan Christensen
Oct 14, 2017, 11:55:18 PM10/14/17
to
On Saturday, October 14, 2017 at 9:09:06 PM UTC-4, Archimedes Plutonium wrote:
> Why No Irrationals exist, and why pi and 2.71… are rational numbers...
The idiocy of the day from Archie Pu! He has the luxury of never having to produce anything that actually works and gets results -- like all the cranks and trolls here. The more outrageous the claim, the better it is to them.
Proof? What's that, eh, Archie?
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
> Why No Irrationals exist, and why pi and 2.71… are rational numbers...
The idiocy of the day from Archie Pu! He has the luxury of never having to produce anything that actually works and gets results -- like all the cranks and trolls here. The more outrageous the claim, the better it is to them.
Proof? What's that, eh, Archie?
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
John Gabriel
Oct 15, 2017, 9:31:27 AM10/15/17
to
On Saturday, 14 October 2017 21:09:06 UTC-4, Archimedes Plutonium wrote:
> Why No Irrationals exist, and why pi and 2.71… are rational numbers
Amazing how deluded you are. pi is not a rational number. It is not a number at all. It is an incommensurable magnitude you poor soul. Tsk, tsk.
> Why No Irrationals exist, and why pi and 2.71… are rational numbers
burs...@gmail.com
Oct 15, 2017, 9:55:51 AM10/15/17
to
Well in modern terminology pi is a number, a real number.
You seem to be the dumbo-maniac here John Gabriel. Maybe
you should hang a plate over your bed that reads:
- irrational numbers = incommensuarble magnitude ratios
- real numbers = irrational number or rational number
here have a banana:
Banana Song (I'm A Banana)
https://www.youtube.com/watch?v=LH5ay10RTGY
John Gabriel you are THE dumbo-maniac, you repeat
the same terminology error again and again.
You seem to be the dumbo-maniac here John Gabriel. Maybe
you should hang a plate over your bed that reads:
- irrational numbers = incommensuarble magnitude ratios
- real numbers = irrational number or rational number
here have a banana:
Banana Song (I'm A Banana)
https://www.youtube.com/watch?v=LH5ay10RTGY
John Gabriel you are THE dumbo-maniac, you repeat
the same terminology error again and again.
burs...@gmail.com
Oct 15, 2017, 10:00:48 AM10/15/17
to
We can alos do it with ZF for you, use the following
set variables:
q : rational numbers
i : irrational numbers
j : icommensuarable magnitude ratios
r : real numbers
We have:
i = j
r = i union q
By the extensionality of set, you should meanwhile
understand what i = j means. Or do you want to continue
your category mistake Mr Dumbo-Maniac?
https://en.wikipedia.org/wiki/Category_mistake
set variables:
q : rational numbers
i : irrational numbers
j : icommensuarable magnitude ratios
r : real numbers
We have:
i = j
r = i union q
By the extensionality of set, you should meanwhile
understand what i = j means. Or do you want to continue
your category mistake Mr Dumbo-Maniac?
https://en.wikipedia.org/wiki/Category_mistake
John Gabriel
Oct 15, 2017, 11:07:03 AM10/15/17
to
On Sunday, 15 October 2017 09:55:51 UTC-4, burs...@gmail.com wrote:
> Well in modern terminology pi is a number, a real number.
No dimwit. In any terminology, pi is a **symbol** or **name** given to an incommensurable magnitude.
> Well in modern terminology pi is a number, a real number.
Learn the difference between magnitude and number. Then and then only might you realise that:
***A number is the MEASURE of a magnitude***
If you claim pi is a number, then show me a number that measures the magnitude circumference length / diameter.
Go on loudmouth!!!
burs...@gmail.com
Oct 15, 2017, 11:10:58 AM10/15/17
to
irrational number = incommensurable magnitude ratio
So its a name of an irrational number.
So its a name of a (real) number.
So its a name of an irrational number.
So its a name of a (real) number.
John Gabriel
Oct 15, 2017, 11:21:07 AM10/15/17
to
On Sunday, 15 October 2017 11:10:58 UTC-4, burs...@gmail.com wrote:
> irrational number = incommensurable magnitude ratio
>
> So its a name of an irrational number.
WRONG.
> irrational number = incommensurable magnitude ratio
>
> So its a name of an irrational number.
>
> So its a name of a (real) number.
>
> Am Sonntag, 15. Oktober 2017 17:07:03 UTC+2 schrieb John Gabriel:
> > On Sunday, 15 October 2017 09:55:51 UTC-4, burs...@gmail.com wrote:
> > > Well in modern terminology pi is a number, a real number.
> >
> > No dimwit. In any terminology, pi is a **symbol** or **name** given to an incommensurable magnitude.
> >
> > Learn the difference between magnitude and number. Then and then only might you realise that:
> >
> > ***A number is the MEASURE of a magnitude***
> >
> > If you claim pi is a number, then show me a number that measures the magnitude circumference length / diameter.
> >
> > Go on loudmouth!!!
burs...@gmail.com
Oct 15, 2017, 11:30:36 AM10/15/17
to
When you say WRONG you only admit that you
are a dumbo-maniac, who cannot use these
two synonyms:
irrational number
incommensurable magnitude ratio
But because of this dumbo-maniac nobody will
think you are the greatest mathematician of
all times, rather everybody things
you are the greatest imbecil of all time.
Here have a banana dumbo:
Of course you also demonstrate that you are
too stupid to use the following common sense
definition, litterally "common" *definition*:
- real numbers = irrational number or rational number
are a dumbo-maniac, who cannot use these
two synonyms:
irrational number
incommensurable magnitude ratio
But because of this dumbo-maniac nobody will
think you are the greatest mathematician of
all times, rather everybody things
you are the greatest imbecil of all time.
Here have a banana dumbo:
Of course you also demonstrate that you are
too stupid to use the following common sense
definition, litterally "common" *definition*:
- real numbers = irrational number or rational number
Zelos Malum
Oct 19, 2017, 12:13:25 AM10/19/17
to
If your term added some kind of subtle distinction it might be worthwhile considering but it doesn't, you are just substituting one word for another and that is not useful in the slightest.
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