My Math Forum Cantors Diagonal Argument for n digits.

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July 14th, 2017, 10:18 AM   #11
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Quote:
 Originally Posted by skipjack Cantor used non-terminating binary sequences, not binary sequences n digits long.
For ALL n.

July 14th, 2017, 10:39 AM   #12
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Quote:
 Originally Posted by zylo For ALL n.
Sure, the number of binary sequences of length n is greater than n, for all n. So what?

July 14th, 2017, 12:01 PM   #13
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Quote:
 Originally Posted by Micrm@ss Sure, the number of binary sequences of length n is greater than n, for all n. So what?
Thanks for acknowledging my assertion.

For all n means no matter how large the sequence is, up to infinity.

So what? So Cantors Diagonal Argument fails, which is consistent with what I show in:
Is an Infinite Binary Sequence a Natural Number?

July 14th, 2017, 12:18 PM   #14
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Quote:
 Originally Posted by zylo Thanks for acknowledging my assertion. For all n means no matter how large the sequence is, up to infinity. So what? So Cantors Diagonal Argument fails, which is consistent with what I show in: Is an Infinite Binary Sequence a Natural Number?
There are no infinite binary sequences in your listing: 0, 1, 00, 01, 10, 11, ...

You're back to banging your head against the wall with the same old nonsense you've brought here time and time again.

I say lock the thread. This is past ridiculous.

July 14th, 2017, 03:34 PM   #15
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 Originally Posted by AplanisTophet I say lock the thread. This is past ridiculous.
Some sites are more freewheeling than others. I like freewheelingness. Nobody is ever obligated to read or respond to any particular post. This site has a fairly permissive moderation policy, that's why I manage to still be here I say let it all hang out and if you don't like someone's posts or threads, don't read them. My 1.999... cents on that.

It's ironic that you in particular would call for the suppression of alternative ideas in which the holder of those ideas seems difficult to reach. I went to quite a lot of trouble to reach you under similar circumstances on at least two different lengthy threads. I didn't call for your threads to be put on hold. I challenged myself to get through to you. Agree?

Some relatively new participants around here have joined us from a far more restrictive site. They must see virtue in the open-mindedness and tolerance for free speech around here, even at the occasional cost of threads that some people don't like.

Besides, aren't these alternative discussions fun? Else why would so many people (generally the same handful of people) invest so much time and energy in acting outraged?

Their other choice would be to just click on something else.

Last edited by Maschke; July 14th, 2017 at 03:49 PM.

July 14th, 2017, 04:44 PM   #16
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Quote:
 Originally Posted by Maschke Some sites are more freewheeling than others. I like freewheelingness. Nobody is ever obligated to read or respond to any particular post. This site has a fairly permissive moderation policy, that's why I manage to still be here I say let it all hang out and if you don't like someone's posts or threads, don't read them. My 1.999... cents on that. It's ironic that you in particular would call for the suppression of alternative ideas in which the holder of those ideas seems difficult to reach. I went to quite a lot of trouble to reach you under similar circumstances on at least two different lengthy threads. I didn't call for your threads to be put on hold. I challenged myself to get through to you. Agree? Some relatively new participants around here have joined us from a far more restrictive site. They must see virtue in the open-mindedness and tolerance for free speech around here, even at the occasional cost of threads that some people don't like. Besides, aren't these alternative discussions fun? Else why would so many people (generally the same handful of people) invest so much time and energy in acting outraged? Their other choice would be to just click on something else.
Your points are well taken. There's a difference between an alternative view though and an unhealthy obsession. I don't believe that these alternative discussions are 'fun' for the person who repeatedly subjects him or herself to them and you need to realize that your amusement here does in fact come at a price. We aren't talking about one thread either. We are talking about many where zylo has been told the same things over, and over, and over again. I am not advocating that this thread be locked because I want to shut zylo up. I am saying it for zylo's own good.

July 14th, 2017, 05:09 PM   #17
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Quote:
 Originally Posted by AplanisTophet Your points are well taken. There's a difference between an alternative view though and an unhealthy obsession.
One man's terrorist is another's freedom fighter. Are you certain that your own early posts came across to every reader as the former and not the latter?

Quote:
 Originally Posted by AplanisTophet I don't believe that these alternative discussions are 'fun' for the person who repeatedly subjects him or herself to them and you need to realize that your amusement here does in fact come at a price. We aren't talking about one thread either. We are talking about many where zylo has been told the same things over, and over, and over again. I am not advocating that this thread be locked because I want to shut zylo up. I am saying it for zylo's own good.
Zylo is a lighting rod for many here. That says more about others than it does about Zylo. One thing Zylo's posts do is expose the weak and shaky understanding of math that some of his most fervent detractors have. After all, the things that most annoy us about others are often aspects of ourselves that we see in them.

I had an interaction with Zylo once where I said to myself:

* I can insult him. That's rude. When X insults Y that tells us something about X and nothing about Y.

* I can ignore him. That's sane. Seven billion people have chosen this path.

* I can try to get through to him and view the exercise as a personal challenge to make my own mathematical exposition so clear that it cannot be denied.

This was a thread discussing the proposition that a function between metric spaces is continuous in the $\epsilon$-$\delta$ sense if and only if it's continuous with respect to the topological definition that the inverse image of an open set is open.

In the course of working with Zylo on this I got my own instincts and intuitions about this theorem as clear as they've ever been since I proved the same thing in real analysis many many (many!) years ago. I ended up drawing a beautiful diagram. I gained a lot from that experience. I enjoyed myself and I ran some math through my head. Isn't that why we're all here?

There are always those three choices: Insult someone who has done nothing to harm you in any way, and is only expressing their truth, as wrong or nonstandard or confused as it may sometimes be; or IGNORE them, which seven billion people walking the earth have managed to do; or challenge the hell out of yourself to create a mathematical exposition that is so clear that it cannot be refuted even by a stubborn doubter.

I offer as evidence this thread.

We have no control over what others say and do, but we can choose who we are in the way we respond. With insults, with apathy, or with self-challenge to perfect our own understanding.

Last edited by Maschke; July 14th, 2017 at 05:26 PM.

July 14th, 2017, 06:00 PM   #18
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Quote:
 Originally Posted by Maschke One man's terrorist is another's freedom fighter. Are you certain that your own early posts came across to every reader as the former and not the latter?
My early posts demonstrated that I lacked a basic understanding of real analysis and further that I'm quite stubborn, but they were also out of a much more general confusion. On the other hand, zylo is trying to contradict a specific theorem over, and over, and over again. I'm not a psychologist, but I'm willing to bet that zylo is struggling here and there is more to the story. It's not about math.

Now, maybe I'm wrong. But, in this case, I don't care to risk that assumption. In fact, I'd argue that by prolonging this (even if well intentioned), you may very well be ignoring zylo in other ways more important and thus have chosen both your second and third options:

Quote:
 Originally Posted by Maschke IGNORE them, which seven billion people walking the earth have managed to do; or challenge the hell out of yourself to create a mathematical exposition that is so clear that it cannot be refuted even by a stubborn doubter.

July 15th, 2017, 03:18 AM   #19
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Quote:
 Originally Posted by zylo For all n means no matter how large the sequence is, up to infinity.
Your example confirmed that Cantor couldn't have used a finite value of n without modifying his procedure. A corresponding example where a finite value of n isn't used (because the sequences are all non-terminating), results in a constructed sequence that isn't amongst the sequences used in the construction, just as Cantor observed.

If n isn't finite, you can't claim that the "number" of non-terminating binary sequences is greater than n without explaining what that would mean.

In a binary sequence, the digits are countable (regardless of whether the sequence terminates). If the "number" of non-terminating sequences is "greater than countable", that's consistent with Cantor's conclusion that the set of all non-terminating sequences isn't countable.

July 15th, 2017, 05:56 AM   #20
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Quote:
 Originally Posted by Maschke Besides, aren't these alternative discussions fun? Else why would so many people (generally the same handful of people) invest so much time and energy in acting outraged?
You aren't above outrage and insults yourself. Nor are you above belittling other's efforts to help in order to demonstrate that you have more advanced knowledge - regardless of context.

As with the other guy this week, this thread serves only two functions: 1) to feed Zylo's ego, because he really isn't interested in listening to counter-arguments about his (nonsensical) theory; and 2) confusing students who happen to look at it. This latter is serious because there's a good chance that such a student is already confused and that that is their reason for stopping by. If Zylo demonstrated any intention to listen to argument and either accept or respond to it, I'd think differently. But as it is this thread should be closed. The suggestion that "for all $n$“ includes infinite values is sufficient to demonstrate that Zylo doesn't know what he's talking about. And the fact that its the umpteenth thread he's started on the subject shows that he isn't interested in engaging with reasoned argument.

It's time to shut this nonsense down.

 Tags argument, cantors, diagonal, digits

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