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Set Theory is Doomed
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FredJeffries
May 20, 2015, 11:24:18 AM5/20/15
to
John Gabriel
May 20, 2015, 12:54:10 PM5/20/15
to
On Wednesday, 20 May 2015 17:24:18 UTC+2, FredJeffries wrote:
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
"Set Theory and a Paradox
Set theory grew out of an impulse to put mathematics on an entirely rigorous footing -- a logical basis even more secure than numbers themselves. Set theory begins with the set containing nothing -- the null set -- which is used to define the number zero. The number 1 can then be built by defining a new set with one element -- the null set. The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1). In this way, each whole number can be defined as the set of sets that came before it."
I want to say that NOTHING is more secure than the Euclidean derivation which I was the FIRST to understand in its entirety. No moron before me even came close to understanding the profound depth of what Euclid was attempting to accomplish, but failed because of Ancient Greek being such a difficult language and the fact that he was the first to ever attempt such a formulation. Euclid has some issues with definitions that are circular. I have corrected all of this. NO computer would ever be able to accomplish what I have done. Well, no human has been able to come even close.
The statement:
"The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1)."
is rather hilarious:
The number 2 is the "empty" brown paper that contains two elements -- an "empty brown paper bag" and the bag that contains the empty brown paper bag(1).
0 = {},
1 = {0} = {{}}
2 = {0,1} = {{},{{}}}
However, a set does not contain the NULL set as an element - ever. The NULL set is by definition a subset! Chuckle.
"But set theory isn't the only way to do mathematics. The proof assistant programs Coq and Agda, for example, are based on a different formal system called type theory."
It's a very bad way of TRYING to do mathematics, but the way mythmaticians do mythmatics! :-)
The author of the article is an absolute idiot just like most of YOU!
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
"Set Theory and a Paradox
Set theory grew out of an impulse to put mathematics on an entirely rigorous footing -- a logical basis even more secure than numbers themselves. Set theory begins with the set containing nothing -- the null set -- which is used to define the number zero. The number 1 can then be built by defining a new set with one element -- the null set. The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1). In this way, each whole number can be defined as the set of sets that came before it."
I want to say that NOTHING is more secure than the Euclidean derivation which I was the FIRST to understand in its entirety. No moron before me even came close to understanding the profound depth of what Euclid was attempting to accomplish, but failed because of Ancient Greek being such a difficult language and the fact that he was the first to ever attempt such a formulation. Euclid has some issues with definitions that are circular. I have corrected all of this. NO computer would ever be able to accomplish what I have done. Well, no human has been able to come even close.
The statement:
"The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1)."
is rather hilarious:
The number 2 is the "empty" brown paper that contains two elements -- an "empty brown paper bag" and the bag that contains the empty brown paper bag(1).
0 = {},
1 = {0} = {{}}
2 = {0,1} = {{},{{}}}
However, a set does not contain the NULL set as an element - ever. The NULL set is by definition a subset! Chuckle.
"But set theory isn't the only way to do mathematics. The proof assistant programs Coq and Agda, for example, are based on a different formal system called type theory."
It's a very bad way of TRYING to do mathematics, but the way mythmaticians do mythmatics! :-)
The author of the article is an absolute idiot just like most of YOU!
Dan Christensen
May 20, 2015, 2:57:16 PM5/20/15
to
On Wednesday, May 20, 2015 at 11:24:18 AM UTC-4, FredJeffries wrote:
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
Where can I find a list of Voevodsky's axioms?
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
Where can I find a list of Voevodsky's axioms?
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
Ross A. Finlayson
May 20, 2015, 8:48:17 PM5/20/15
to
What is the Univalent axiom
in the language of set theory
besides Skolem, Cohen, and an
application note in the language
of type theory?
You can already be building
it in set theory, for example
with measure theory.
The note is that model extension
for fibration, and Dirichlet forcing
for regularity (not set-theoretic,
number-theoretic) then that the
foundation is a definition of
measure for the usual analytical
origin.
Rather, that's in the language
of set theory.
in the language of set theory
besides Skolem, Cohen, and an
application note in the language
of type theory?
You can already be building
it in set theory, for example
with measure theory.
The note is that model extension
for fibration, and Dirichlet forcing
for regularity (not set-theoretic,
number-theoretic) then that the
foundation is a definition of
measure for the usual analytical
origin.
Rather, that's in the language
of set theory.
Ross A. Finlayson
May 20, 2015, 8:53:07 PM5/20/15
to
No, set theory is not "doomed".
Dan Christensen
May 20, 2015, 10:29:20 PM5/20/15
to
On Wednesday, May 20, 2015 at 11:24:18 AM UTC-4, FredJeffries wrote:
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
See Andrej Bauer, "Univalent foundations subsume classical mathematics" at http://math.andrej.com/2014/01/13/univalent-foundations-subsume-classical-mathematics/
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
If so, then set theory is definitely NOT doomed.
Ross A. Finlayson
May 20, 2015, 10:45:22 PM5/20/15
to
Yeah: "conservativity results".
Dan Christensen
May 20, 2015, 10:47:42 PM5/20/15
to
On Wednesday, May 20, 2015 at 12:54:10 PM UTC-4, John Gabriel wrote:
> On Wednesday, 20 May 2015 17:24:18 UTC+2, FredJeffries wrote:
> > https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
>
> "Set Theory and a Paradox
>
> Set theory grew out of an impulse to put mathematics on an entirely rigorous footing -- a logical basis even more secure than numbers themselves. Set theory begins with the set containing nothing -- the null set -- which is used to define the number zero. The number 1 can then be built by defining a new set with one element -- the null set. The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1). In this way, each whole number can be defined as the set of sets that came before it."
>
> I want to say that NOTHING is more secure than the Euclidean derivation which I was the FIRST to understand in its entirety. No moron before me even came close to understanding the profound depth of what Euclid was attempting to accomplish, but failed because of Ancient Greek being such a difficult language and the fact that he was the first to ever attempt such a formulation. Euclid has some issues with definitions that are circular. I have corrected all of this.
You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
> On Wednesday, 20 May 2015 17:24:18 UTC+2, FredJeffries wrote:
> > https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
>
> "Set Theory and a Paradox
>
> Set theory grew out of an impulse to put mathematics on an entirely rigorous footing -- a logical basis even more secure than numbers themselves. Set theory begins with the set containing nothing -- the null set -- which is used to define the number zero. The number 1 can then be built by defining a new set with one element -- the null set. The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1). In this way, each whole number can be defined as the set of sets that came before it."
>
> I want to say that NOTHING is more secure than the Euclidean derivation which I was the FIRST to understand in its entirety. No moron before me even came close to understanding the profound depth of what Euclid was attempting to accomplish, but failed because of Ancient Greek being such a difficult language and the fact that he was the first to ever attempt such a formulation. Euclid has some issues with definitions that are circular. I have corrected all of this.
> NO computer would ever be able to accomplish what I have done.
John Gabriel
May 20, 2015, 11:24:03 PM5/20/15
to
On Thursday, 21 May 2015 04:47:42 UTC+2, Dan Christensen wrote:
> On Wednesday, May 20, 2015 at 12:54:10 PM UTC-4, John Gabriel wrote:
> > On Wednesday, 20 May 2015 17:24:18 UTC+2, FredJeffries wrote:
> > > https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
> >
> > "Set Theory and a Paradox
> >
> > Set theory grew out of an impulse to put mathematics on an entirely rigorous footing -- a logical basis even more secure than numbers themselves. Set theory begins with the set containing nothing -- the null set -- which is used to define the number zero. The number 1 can then be built by defining a new set with one element -- the null set. The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1). In this way, each whole number can be defined as the set of sets that came before it."
> >
> > I want to say that NOTHING is more secure than the Euclidean derivation which I was the FIRST to understand in its entirety. No moron before me even came close to understanding the profound depth of what Euclid was attempting to accomplish, but failed because of Ancient Greek being such a difficult language and the fact that he was the first to ever attempt such a formulation. Euclid has some issues with definitions that are circular. I have corrected all of this.
>
> You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
You need proof for mythmatics, but you don't need any proofs for 2+2=4 in real mathematics. While it is very easy to prove using my axioms of arithmetic, 2+2 is just the definition of 4. You can't grasp this because you are too stupid.
> On Wednesday, May 20, 2015 at 12:54:10 PM UTC-4, John Gabriel wrote:
> > On Wednesday, 20 May 2015 17:24:18 UTC+2, FredJeffries wrote:
> > > https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
> >
> > "Set Theory and a Paradox
> >
> > Set theory grew out of an impulse to put mathematics on an entirely rigorous footing -- a logical basis even more secure than numbers themselves. Set theory begins with the set containing nothing -- the null set -- which is used to define the number zero. The number 1 can then be built by defining a new set with one element -- the null set. The number 2 is the set that contains two elements -- the null set (0) and the set that contains the null set (1). In this way, each whole number can be defined as the set of sets that came before it."
> >
> > I want to say that NOTHING is more secure than the Euclidean derivation which I was the FIRST to understand in its entirety. No moron before me even came close to understanding the profound depth of what Euclid was attempting to accomplish, but failed because of Ancient Greek being such a difficult language and the fact that he was the first to ever attempt such a formulation. Euclid has some issues with definitions that are circular. I have corrected all of this.
>
> You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
Carry on reading Godel who thinks that "recursion" makes a formal system strongly representable. Chuckle.
"The Representability Theorem
In any consistent formal system which contains Q:
A set (or relation) is strongly representable if and only if it is recursive;
A set (or relation) is weakly representable if and only if it is recursively enumerable."
What a load of Godel BS. Recursion is implemented by use of PUSH/POP directives in most processor architecture. It makes a real-time system with synchronisation objects very unstable. Imagine two separate threads A and B calling a factorial() function that has been implemented recursively.
Thread A pushes its formal arguments (if any) onto stack, its return address and then calls factorial(). Inside factorial(), local variables are pushed on the stack as well for each call. These are preserved on the stack for A and B. Some instance during A's processing, B calls factorial(). Boom! So much for "recursive stability".
What I just described is an actual experience. What happened was that the recursive function would not compute properly, sometimes it did and other times it crashed. I implemented it without recursion and it worked just fine. In fact, recursion is cleaner if the stack is not used, rather an array of structures as follows:
{ Function Identifier, Call number, args, local vars }
It's a little more processing but far more stable since B cannot pop A's return address or vice-versa. Also, neither thread can use the other's local variables.
Non-recursive algorithms are far more stable. Goedel and all the recursion addicts were a bunch of effed up morons like you. "That's so Koool!" - the typical immature American/Canadian frame of mind. Tsk, tsk.
So much for Godel's "Representability Theorem".
Troll DC is still struggling to understand the following statement:
1/3 is the measured magnitude but 1:3 is the ratio of the magnitudes being compared. Division has already taken place in 1/3. Nothing more to do. It's a number. 1 -:- 3 is an algorithm that does NOTHING in algebra. It has come to mean 1 divided by 3, but it's only possible using geometry.
Idiot will probably come back with something like 1/3 * 3 = 1, forgetting that there are a lot of assumptions already in that statement that he hasn't proved.
Chuckle.
>
>
> > NO computer would ever be able to accomplish what I have done.
>
> Hint: If you cannot "computerize" your system, it is probably not a workable foundation for mathematics. To paraphrase Albert Einstein, if you can't "explain it" to a computer, you don't understand it yourself.
Dan Christensen
May 21, 2015, 12:55:27 AM5/21/15
to
On Wednesday, May 20, 2015 at 11:24:03 PM UTC-4, John Gabriel wrote:
> > You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
>
> You need proof for mythmatics, but you don't need any proofs for 2+2=4 in real mathematics.
It's a test of your system -- a test your goofy system obviously fails.
> > You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
>
> You need proof for mythmatics, but you don't need any proofs for 2+2=4 in real mathematics.
> While it is very easy to prove using my axioms of arithmetic, 2+2 is just the definition of 4.
How many "definitions" of 4 do you have in your system, Troll Boy?
0+4=4, 1+3=4, 2+2=4, 3+1=4, 5-1=4, 6-2=4, ....????
There is only one definition of 4 in my system, namely 3+1=4. Now, how to go from the definitions of 1, 2, 3 and 4 to 2+2=4? Apparently impossible in your goofy system.
> >
> > > NO computer would ever be able to accomplish what I have done.
> >
> > Hint: If you cannot "computerize" your system, it is probably not a workable foundation for mathematics. To paraphrase Albert Einstein, if you can't "explain it" to a computer, you don't understand it yourself.
>
> A computer cannot think!
Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
The JG Really Stupid Quote of the Day:
"I am the last word on everything."
-- John Gabriel, May 6, 2015
"Unless I think it's logic, it's not... There are no rules in mathematics... As I have repeatedly stated, if there were to be rules, I'd be making the rules."
-- John Gabriel, March 17, 2015
Dan Christensen
May 21, 2015, 1:07:18 AM5/21/15
to
On Wednesday, May 20, 2015 at 11:24:03 PM UTC-4, John Gabriel wrote:
>
> 1/3 is the measured magnitude but 1:3 is the ratio of the magnitudes being compared. Division has already taken place in 1/3. Nothing more to do. It's a number. 1 -:- 3 is an algorithm that does NOTHING in algebra. It has come to mean 1 divided by 3, but it's only possible using geometry.
>
Troll Boy is still struggling with basic 3rd grade arithmetic. He still cannot figure out why 1 -:- 3 = 1/3. Very sad indeed.
>
> 1/3 is the measured magnitude but 1:3 is the ratio of the magnitudes being compared. Division has already taken place in 1/3. Nothing more to do. It's a number. 1 -:- 3 is an algorithm that does NOTHING in algebra. It has come to mean 1 divided by 3, but it's only possible using geometry.
>
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
May 21, 2015, 2:53:31 AM5/21/15
to
On Thursday, 21 May 2015 06:55:27 UTC+2, Dan Christensen wrote:
> On Wednesday, May 20, 2015 at 11:24:03 PM UTC-4, John Gabriel wrote:
>
> > > You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
> >
> > You need proof for mythmatics, but you don't need any proofs for 2+2=4 in real mathematics.
>
> It's a test of your system -- a test your goofy system obviously fails.
Bullshit. It's part of the derivation of natural numbers from ratios of magnitudes. That's something NO ONE before me has been able to comprehend.
> On Wednesday, May 20, 2015 at 11:24:03 PM UTC-4, John Gabriel wrote:
>
> > > You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
> >
> > You need proof for mythmatics, but you don't need any proofs for 2+2=4 in real mathematics.
>
> It's a test of your system -- a test your goofy system obviously fails.
Euclid is hard reading and even when you're Greek, it's a long road...
> > While it is very easy to prove using my axioms of arithmetic, 2+2 is just the definition of 4.
>
> [snip]
>
> How many "definitions" of 4 do you have in your system, Troll Boy?
>
> 0+4=4, 1+3=4, 2+2=4, 3+1=4, 5-1=4, 6-2=4, ....????
> There is only one definition of 4 in my system, namely 3+1=4.
Now pay attention moron: 3+1 = 2+1+1 = 1+1+1+1
Guess what? Recursion doth not plagiarism prevent. Guissepe the peppe, was a fool. You have been fooled by a fool. That makes you twice the fool he was, at least!
> Now, how to go from the definitions of 1, 2, 3 and 4 to 2+2=4? Apparently impossible in your goofy system.
>
>
> > >
> > > > NO computer would ever be able to accomplish what I have done.
> > >
> > > Hint: If you cannot "computerize" your system, it is probably not a workable foundation for mathematics. To paraphrase Albert Einstein, if you can't "explain it" to a computer, you don't understand it yourself.
> >
> > A computer cannot think!
>
> Something you can identify with, eh, Troll Boy? Didn't think you would get that one. Oh, well.
How's DCMisproof sales now days? Chuckle. Anyone downloading your shit? Bad news for you: my New Calculus gets thousands of hits from ALL over the planet, from every corner of the world. Gee, that's much better than the best journal can do where those reading my work are the likes of you and the old fool dullrich. Hee, hee.
Dan Christensen
May 21, 2015, 9:43:50 AM5/21/15
to
On Thursday, May 21, 2015 at 2:53:31 AM UTC-4, John Gabriel wrote:
> > > > You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
> > >
> > > You need proof for mythmatics, but you don't need any proofs for 2+2=4 in real mathematics.
> >
> > It's a test of your system -- a test your goofy system obviously fails.
>
> Bullshit. It's part of the derivation of natural numbers from ratios of magnitudes. That's something NO ONE before me has been able to comprehend.
>
Call it a derivation or a proof. It doesn't matter. Put up or shut up, Troll Boy.
> > > > You STILL have a long way to go with your new system, JG. We are STILL waiting, for example, for your proofs that 2+2=4 and that 1 divided by 3 is 1/3. If your system cannot handle basic arithmetic like this, it will never handle calculus.
> > >
> > > You need proof for mythmatics, but you don't need any proofs for 2+2=4 in real mathematics.
> >
> > It's a test of your system -- a test your goofy system obviously fails.
>
> Bullshit. It's part of the derivation of natural numbers from ratios of magnitudes. That's something NO ONE before me has been able to comprehend.
>
> > > While it is very easy to prove using my axioms of arithmetic, 2+2 is just the definition of 4.
> >
> > [snip]
> >
> > How many "definitions" of 4 do you have in your system, Troll Boy?
> >
> > 0+4=4, 1+3=4, 2+2=4, 3+1=4, 5-1=4, 6-2=4, ....????
>
> ONE DEFINITION: 1+1+1+1
>
> > There is only one definition of 4 in my system, namely 3+1=4.
>
>
> Now pay attention moron: 3+1 = 2+1+1 = 1+1+1+1
>
Good, we agree on the definition of 4. Now, what about 2+2=4? Do you really think the above is a "proof"?
>
>
> > Now, how to go from the definitions of 1, 2, 3 and 4 to 2+2=4? Apparently impossible in your goofy system.
>
> It's like talking to a monkey when I explain this to you. You can't understand it because there is a huge gulf in our intelligence.
> >
> >
> > > >
> > > > > NO computer would ever be able to accomplish what I have done.
> > > >
> > > > Hint: If you cannot "computerize" your system, it is probably not a workable foundation for mathematics. To paraphrase Albert Einstein, if you can't "explain it" to a computer, you don't understand it yourself.
> > >
> > > A computer cannot think!
> >
> > Something you can identify with, eh, Troll Boy? Didn't think you would get that one. Oh, well.
>
> Meh. Stupid. Everyone knows you are a crank and a failure.
>
> Bad news for you: my New Calculus gets thousands of hits from ALL over the planet, from every corner of the world.
It's too bad then that hits don't translate into followers. At last count, since you first started flogging this still-born horse of yours in 1974 (date from your silly website), you have amassed an international following of, oh let's see... maybe ONE? That retired machinist somewhere in Germany? Unless you are also counting sci.math's own, your fellow troll, Wolfgang Mueckenheim (WM). I'm sorry to say, but if you asked either of them, what is 1 divided by 3, I am quite sure both would say 1/3. So, probably not a single follower of your wacky new system on the entire planet in 41 years. Very sad indeed. Or it would be if you weren't such an a**hole.
Do you really want to waste what's left of your life on this useless system of yours, Troll Boy? Time to cut your losses and move on.
John Gabriel
May 21, 2015, 10:07:37 AM5/21/15
to
On Wednesday, 20 May 2015 17:24:18 UTC+2, FredJeffries wrote:
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
So tell us, what do you think? If anything at all... Chuckle.
> https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/
Ross A. Finlayson
May 21, 2015, 6:50:15 PM5/21/15
to
You might notice that defining
the Univalency axiom and defining
sweep, the natural/unit equivalency function, are the same.
This with the existence result
of the regular fibration of
"univalency" (unitarity) or the
differential components of unit,
bringing measure theory down from "foundations" is already from where
it was from "above", in the
foundations. Defining measure
theory before set theory is not
much changing where it is defined
after.
Then this is where the sweep
principle in conservation in
foundations: is already defined
from lesser foundation.
In types, for inverting the diamond
and Russell's types as of set theory, here it is a bold claim of
axiomatization with the resulting
immediate contradictions and
counterexamples from the
standard, "Univalency" should be
pointed out to only hold true for
differentiable systems (no new
features of real analysis from set
theory mute on measure theory),
counter-framework in example.
the Univalency axiom and defining
sweep, the natural/unit equivalency function, are the same.
This with the existence result
of the regular fibration of
"univalency" (unitarity) or the
differential components of unit,
bringing measure theory down from "foundations" is already from where
it was from "above", in the
foundations. Defining measure
theory before set theory is not
much changing where it is defined
after.
Then this is where the sweep
principle in conservation in
foundations: is already defined
from lesser foundation.
In types, for inverting the diamond
and Russell's types as of set theory, here it is a bold claim of
axiomatization with the resulting
immediate contradictions and
counterexamples from the
standard, "Univalency" should be
pointed out to only hold true for
differentiable systems (no new
features of real analysis from set
theory mute on measure theory),
counter-framework in example.
Ross A. Finlayson
May 21, 2015, 7:15:34 PM5/21/15
to
No, homotopy type theory is not "doomed".
abu.ku...@gmail.com
May 21, 2015, 9:04:49 PM5/21/15
to
you seem to ahve failed to read book 7,
where the method of Eudoxus is shown
where the method of Eudoxus is shown
John Gabriel
May 22, 2015, 6:35:22 AM5/22/15
to
abu.ku...@gmail.com
May 22, 2015, 4:49:25 PM5/22/15
to
he couldn't seem to handle the mehtod of Eudozus,
the 1st time that he tried it, and gave "up
the 1st time that he tried it, and gave "up
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