TonesInDeepFreeze

Given any function f from N to , the diagonal proof constructs a member of that is not in the range of f. I feel pretty safe in thinking that you don'...

Do you mean to suggest that there is a 1-1 function from N onto 0? By the way, you claimed that I have no sense of humor. Well, you haven't said anyth...

Start by adopting a specific definition of 'the continuum'. The term is often used flexibly, but I would settle on the continuum understood to be the ...

I told you. You don't have proof of it. You only think you do. Also, you have a serious problem when it's pointed out to you that you are in contradic...

I cherish the mysteries of mathematics. That is not impaired by formalization. On the contrary, formalization leads to even deeper mysteries for me.

(1) How do you know that unless you've interviewed mathematicians about it? (2) I highly doubt that mathematicians very much regret whatever such loss...

That's almost a good example. But it's better described as the centuries-ago formulations being more than vague intuitions yet not adequately formaliz...

Yet you reject other theorems from the same axioms.

You keep saying that. It's dogmatism. In thinking that the fact that in your own mind you imagine that it must be so implies a mathematical proof. And...

Then I bet you really would not like Banach-Tarski. Anyway, stepping back, do you understand the proof of the equinumerosity of N and NxN?

By "the rest of what you posted" I meant the rest of what you posted in that post, just as I was responding exactly to your complaint that I hadn't qu...

True, there are other proofs of the uncountability of . Cantor gave one of those other proofs. There is no map from N^3 onto R. And even if there were...

You have not shown any dogmatism by me. Nor any exclusion other than of ignorant confusion and misinformation. It shows that is uncountable by showing...

Just now, and in the other thread that was deleted yesterday.

The diagonal proof shows that any map from N to R is not onto R. That is, there are real numbers not mapped to.

Whatever you mean by an ordered pair being "contained" in a number, what we have is each number mapped to an ordered pair. The claim of the prover is ...

Yes, a pair of numbers. Not a number as you wrote. You keep resorting to saying that I must consider the rest of what you posted. But each time it tur...

Example?

I have never had any such impression. Very much to the contrary.

To know, we would have to have access to the mental states of mathematicians. We would have to know how long was the time between their first pre-form...

. That is not a real number, you understand, right?

No way. One can offer alternative systems; I enjoy reading about them if they are rigorous. And one can even stipulate one's own terminology, and if i...

Name one.

The problem is not so much that you don't take it seriously, but that you take it seriously enough to stubbornly persist in claims that are false or j...

I resist misinformation.

And you desperately need one if you are not to remain mired in your terrible confusions.

You still demonstrate that you don't understand these basic concepts.

There you go what? I am the first to say that one has to use great caution trying to pick up math on the Internet. There are some excellent Internet s...

I redid the post.

So? Not everything on the Internet is the sharpest formulation.

EDIT: That's not quite right since it has free variables on the right that aren't on the left. f is onto Y if and only if (f is a function & range(f)=...

As I said, you don't know the meaning of 'onto' in mathematics. Or you're insane.

So which is it now? You claim that card(R) = aleph_1, thus asserting the continuum hypothesis? Or you deny that card(R) = aleph_1, thus denying the co...

Either you are insane or you don't know the meaning of 'map onto'.

So you are in flat out contradiction with yourself.

Of course one can map a singleton set INTO R. But there is no map of N ONTO R.

Yet you say you disagree with the continuum hypothesis now, while you have been claiming it in dozens and dozens of posts.

The number 0 is not a riddle.

Great. And I can make the sun disappear by wiggling my ears.

Then what do you mean? Why won't you now look up 'continuum hypothesis'?

So what? This is not a game with a scoreboard for how many questions I've answered. Anyway, I've addressed TONS of your claims.

So years ago you looked it up, but still don't understand it now. You don't agree with "it"? The continuum hypothesis? You have been claiming the cont...

I really would rather not know about the bedtimes of you and your wife.

Not at all. It's telling that you could figure out for yourself, but you won't, that your claim is false for the simple reason that I have not just gi...

Eliza is now all tangled up in confusion. My answer was to the question about mappings from N onto not about why your claim that I have done nothing b...

Eliza is getting tired and reduced to token replies.

That you don't understand the answer is not my problem. I did answer it. Now your turn to answer my question,.

The claim you made, as I quoted it, silly.

Now you have flat out lied. Again now, your turn to answer my question.