## Cantor Diagonal Argument disproof

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### Re: Cantor Diagonal Argument disproof

JeffJo wrote:In physics, yes, the PARAMETRIC EQUATIONS define paths. Points themselves don't. And besides, this is Math Class.robert 46 wrote:JeffJo wrote:They do with parametric equations such as the functions x(t), y(t), z(t) producing the position of a point in time.

What part of parametric equations is not mathematical?

There certainly is. Points are not "put" anywhere. They ARE the endpoints of line segments.There is no disagreement that points can be put on a line.

If a line is y=m*x+b then if p1=(x1,y1) and p2=(x2,y2) are two points which satisfy the equation then they are put on the line to define a line segment.

Then it's a good thing that the Axiom of Infinity, and the Diagonalization Theorem, belong to Axiomatic Set Theory,, isn't it?Naïve set theory was loaded with contradictions. You can define a fantasy as rigorously as you like, but that doesn't mean it is sensible.

Not considering that there are set theories with and without the Axiom of Choice.

robert was, and still is, evading the question. Are there, or are there not, more line segments in [0,1] than in [0,10]? Explain all you want, but provide a yes or no with it.I was showing that JeffJo was setting up a trick question.

You have said that "yes" and "no" are both valid answers, so I have no interest in choosing one.

You mean, like you are doing now? To evade the question?Where an answer is "yes and no" there must be an equivocation.

I invite you to explain the equivocation which gives both "yes" and "no" answers.

Because when you don't have them, you get your nonsensical answers.So why does a system need to have infinite sets???

JeffJo's projection. Finitists disagree.

Only if you refuse to grasp the point that infinite segments, and "infinite+1" (whatever that is supposed to mean) endpoints is the nonsensical part.Thank you for finally expressing that thought,

Ambiguous as to which thought JeffJo is referring.

Well, I said it was nonsensical.

No, recall that what we are interested is defining an example,and showing why a Mathematics based on "actually producing" every element t of such a set is "nonsensical".

Recall that we are interested in producing an example, or producing an algorithm which would produce an example.

Well, anyone can define a unicorn however they like.

and that robert refuses to define what he thinks "producing" and "algorithm" mean, or why these undefined concepts are superior to a Mathematically valid algoritm that defines an infinite string.. He just insists that Cantor didn't do it, but won't say what was not done.

What was not done is get to the end of an endless list to produce a string ~D. What was done is define having gotten to the end of an endless list to define a string ~D. Baum defined a tornado taking Dorothy and Toto to the land of Oz to meet the wizard.

The nth character of ~D is the opposite character of the nth character of the nth string in the mapping we assume exists. There is no part of ~D that is not "produced" by this well-defined algorithm; it is just a random-access algorithm instead of the sequential one robert seems to think is needed, but refuses to explain why.

Because there is no reason to think that an endless parallel access is any more valid than an endless sequential access.

- robert 46
- Intellectual
**Posts:**2849**Joined:**Mon Jun 18, 2007 9:21 am

### Re: Cantor Diagonal Argument disproof

Robert uses many ploys to evade a point he can't address. One is misdirection:

A other ploy is misinterpretation:

And the point here, that robert is trying to brush under the rug, is that the parametric form y=m*x+b does define every possible point, in the Mathematical sense. An infinity of them in a continuum, on the line. His point was that Physics may not recognize all of them, which is irrelevant. As was bringing up space-time.

Here's misinterpretation mixed with another ploy, contradicting positions he has claimed before:

And then there is pure evasion:

Then there's parroting, with changed meaning:

Yet another ploy is ignoring facts by calling them "projection"

More evasion:

And yet another ploy is evasion by hyberbole:

I'll ignore the hyperbole in that part. It's just more evasion.

The equations themselves? No part. What is being modeled? All of it. Math is the tool the Physics uses to model the universe.robert 46 wrote:What part of parametric equations is not mathematical?

A other ploy is misinterpretation:

If y1=m*x1+b, then it is on that line whether or not you express it in an equation.There certainly is. Points are not "put" anywhere. They ARE the endpoints of line segments.There is no disagreement that points can be put on a line.

If a line is y=m*x+b then if p1=(x1,y1) and p2=(x2,y2) are two points which satisfy the equation then they are put on the line to define a line segment.

And the point here, that robert is trying to brush under the rug, is that the parametric form y=m*x+b does define every possible point, in the Mathematical sense. An infinity of them in a continuum, on the line. His point was that Physics may not recognize all of them, which is irrelevant. As was bringing up space-time.

Here's misinterpretation mixed with another ploy, contradicting positions he has claimed before:

So is robert finally admitting that Mathematics is not a single field of study, but is based on the axioms one choses to accept? But note that the Axiom of Choice is the "C" in ZFC, or Zermelo–Fraenkel set theory with the axiom of choice. Which includes the Axiom of Infinity, and Cantor Diagonalization as a theorem. As does plain ZF.Not considering that there are set theories with and without the Axiom of Choice.

And then there is pure evasion:

I have said they are both valid in Cantor's mathematics. Robert uses a different Mathematics, which he won't define. In it, the answer to the question has to be one, or the other. So robert uses any excuse he can to not answer.You have said that "yes" and "no" are both valid answers, so I have no interest in choosing one.

Then there's parroting, with changed meaning:

I have. In modern set theory, an infinite set can be matched 1:1 with a strict subset of itself. This allows it to be considered, by robert's implied definitions, any of larger, smaller, or the same size as itself. The flaw isn't the theory of infinite sets, it is trying to use robert's unstated, but necessarily flawed definitions of what '"larger, smaller, or the same size" means with them. And this is why robert needs to answer the question with either yes or no, or explain how both can be true (which he has denied).I invite you to explain the equivocation which gives both "yes" and "no" answers.

Yet another ploy is ignoring facts by calling them "projection"

Finitists are the ones who can't answer the question I asked, so their mathematics is flawed.Because when you don't have them, you get your nonsensical answers.So why does a system need to have infinite sets???

JeffJo's projection. Finitists disagree.

More evasion:

And I said it was the form of robert's question, not the concept robert was criticizing, that was non-sensical.Well, I said it was nonsensical.

And yet another ploy is evasion by hyberbole:

The issue robert evades here is that he refuses to define the procedures he insists Cantor's theorem must follow. The definitions he compares to imaginary creatures are the quite real, and valid, definitions that robert doesn't want to accept.Well, anyone can define a unicorn however they like.

What is done, is the provision of an algorithm that is capable of "producing" any character in the string. What is not done by robert, is justifying why it has to be "produced" sequentially, what he means by reaching the end of an endless list, or how he can assume the existence of the endless list that is required as input to the algorithm, when he insists on this absurd requirement.What was not done [by Cantor] is get to the end of an endless list to produce a string ~D.

I'll ignore the hyperbole in that part. It's just more evasion.

There is also no reason to think it is less valid. At least, robert hasn't even attempted to provide one, only to assert that sequential access is required.Because there is no reason to think that an endless parallel access is any more valid than an endless sequential access.

- JeffJo
- Intellectual
**Posts:**2609**Joined:**Tue Mar 10, 2009 11:01 am

### Re: Cantor Diagonal Argument disproof

WARNING: DO NOT CLICK ON THE LINKS IN THE ABOVE POST.

It may be a dangerous website. I have noticed this activity of posting links to hidden websites for some months, and wonder if its purpose is to infect computers with a Trojan horse through some identified vulnerability for a future cyber attack.

If it is merely advertising for on-line gambling then consider this: If you don't know whether you can trust a casino to be honest, then what makes you think an on-line gambling site thousands of miles away in India is going to be honest???

My father occasionally was in the Bahamas with friends, and whereas the Bahamas had legal casinos, he would bet in a small way for entertainment. He would bet at the roulette wheel, which has the lowest take for the house of all gambling games, and would always bet against the "high rollers". The theory was that if the casino was cheating it would do so against the high bettors occasionally so that it would not become obvious. By this method, he would win around $50 during the night, and then use the money to buy champagne for his friends. A good time was had by all in his party. As for the "high rollers", he never bothered to find out how well or poorly they had done by the end of the night.

It may be a dangerous website. I have noticed this activity of posting links to hidden websites for some months, and wonder if its purpose is to infect computers with a Trojan horse through some identified vulnerability for a future cyber attack.

If it is merely advertising for on-line gambling then consider this: If you don't know whether you can trust a casino to be honest, then what makes you think an on-line gambling site thousands of miles away in India is going to be honest???

My father occasionally was in the Bahamas with friends, and whereas the Bahamas had legal casinos, he would bet in a small way for entertainment. He would bet at the roulette wheel, which has the lowest take for the house of all gambling games, and would always bet against the "high rollers". The theory was that if the casino was cheating it would do so against the high bettors occasionally so that it would not become obvious. By this method, he would win around $50 during the night, and then use the money to buy champagne for his friends. A good time was had by all in his party. As for the "high rollers", he never bothered to find out how well or poorly they had done by the end of the night.

- robert 46
- Intellectual
**Posts:**2849**Joined:**Mon Jun 18, 2007 9:21 am

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