TonesInDeepFreeze

Not the zillionth time, but it is the second time you have made that false claim.

No one ever told you that mathematics is not throwing around words like 'conformal' while not knowing what they mean.

I answered one of your questions. Your turn to answer one of mine.

I do. You don't conversely. Read not just what I write, but what is written anywhere you would look: There is no bijection between N and . What you wr...

You contradict yourself. You claim there is a bijection from N onto R, but above you admit that the interval is uncountable. And we don't write '' to ...

That is purely arbitrary unfounded assertion. On the other hand, in set theory, from rigorously stated axioms, definitions, and rules of inference we ...

Every cardinal is either countable or uncountable. Every countable cardinal is either finite or denumerable. There are denumerably many countable card...

Wrong. For any infinite set S.

Do you mean N onto R? The answer is 0. My many previous remarks amply imply that. Now that I've answered your question, howzabout you answering a ques...

CORRECTION to the post below. This answers proving that card(R) = card(RxR), which is not what was asked of me. Instead, what was asked of me is "how ...

I'm embarrassed. "Heat Wave" is by Irving Berlin not Cole Porter.

Incorrigible.

I already explained to you that proving that there is a bijection from N onto R requires stating your axioms, definitions, and rules of inference and ...

You haven't proven any math. But you have proven yourself to be a crank.

I didn't say I gave you functions. And I have never said anything about repeated fractions. You seem to have confused me with another poster.

I'll give you a point for that one.

"She certainly can-can." - Cole Porter

I don't know whether the following post by me appeared in the thread that was deleted today: Take away the word 'project' (a projection function is a ...

Disgusting.

So what? In general geniuses drink water. I drink water. That doesn't make me a genius. In an any case, you show no evidence of genius. Very much to t...

Algorithm for Eliza: Step 1. Open browser. Step 2. In the search field, type: continuum hypothesis Step 3. Click on the first link that appears to be ...

Fraenkel and Zermelo. Aren't they that old vaudeville comedy team that played the Borscht Belt years ago? But I thought maybe you meant Frank Zappa. H...

By the way, I did look at that Quora page you suggested in the thread that has since been deleted. The first post there is a proof that card(R) = card...

In another thread in which you were posting, I already wrote that I am not an expert. It doesn't highlight any concept. It only highlights that you do...

Indeed I have a different notion from yours! My notion is the usual one in mathematics. You, on the other hand, are unfamiliar with the ordinary mathe...

Which has no apparent meaning. I guess what you mean is SxS where S is infinite. But then there are more than card(NxN) real numbers between 0 and 1. ...

Yes, my mistake about the link to Feedback.

"inf^2" is not a recognizable notion. Probably what you mean is 2^N. And you ignorantly, wantonly persist about aleph_1 The claim that aleph_1 = 2^N i...

I am not venting. I am expressing my thoughts about it to you and whomever might be interested. As you and another poster have mentioned your thoughts...

You are errant in so many ways: (1) My responses decidedly were usually not merely brief and not lacking content. (2) My latest response did include m...

Without warning, without notification, without explanation. Is that not rude and arrogant moderation? What is the explanation anyway?

I can't find the recent thread about the Russell set. And when I click the link to 'Feedback' it does nothing.

I have not mentioned continuousness. I have merely pointed out the utterly well known fact that it is a theorem that card(R) = card(RxR),. That is ris...

It is a theorem that card(R) = card(R^n) for any natural number n>0. This is known by anyone who has read a basic textbook in set theory. Just read th...

'the continuum' is probably most exactly defined as <R less_than>, but let's simplify here to just say it's R. It is the continuum hypothesis that its...

He says he's out of his depth but persists by positing an "update". The update is nonsense updating nonsense. Meanwhile, he's not the least bit intere...

The three books mentioned above are well beyond the preparedness of anyone who has not studied at least basic symbolic logic. The best book for the la...

The Godel sentence is a formula in the language of formal arithmetic. It an exact formula using only the symbols of symbolic logic and the symbols of ...

What? .999... is not a sequence. It's a number. That number is 1. The sequence is {<1 9/10> <2 99/100> <3 999/1000>...} and its limit is 1. Once more:...

You keep replying past the simple straightforward points I made. Especially again as you go past my point that you haven't mathematically defined "rea...

Of course, if the sequence does not converge then it's another ballgame. But we easily prove that the sequence we've been talking about does converge....

By the way, when I say that non-standard analysis is subsumed within classical mathematics, I mean non-standard analysis developed in ZFC. I'm not ref...

Specifically, we don't do that even in simple freshman calculus. I have never read an author say there is an "implicit reaching" (whatever that would ...

Of course non-standard has infinitesimals. (And non-standard analysis takes place itself in a larger environment of classical mathematics.) Though, I ...

What do you mean by 'instantiating infinity'. We instantiate the set of natural numbers in set theory, of course. And we instantiate the set of ration...

What exactly do you disagree with in what I just posted?

I've not seen it phrased that way, especially in a rigorous exposition in classical mathematics. Not even in freshman calculus. I don't know what writ...

There is an infinite sequence and there is the limit of that infinite sequence. There is no supertask - no performing an infinite number of operations...

Informally inconsistent, yes. Anyway, when we move beyond child-level thinking that there must be involved a "reaching" and instead we study rigorous ...

To be in agreement, you'd have to agree that the limit of the sequence is rigorously defined.