how many times you can map N on R — AgentTangarine

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 question I've been asking you: Why won't look up 'continuum hypothesis' on the Internet?

That's for countable sets. — AgentTangarine

Wrong. For any infinite set S.

It's not so complicated as they make it. There are basically two types of infinities. Infinite countable infinities, like N and infinite times infinite types. Like the interval [0-1]. Uncountable. All alephs are multiplicities of them.

Wrong. For any infinite set S. — TonesInDeepFreeze

And that's exactly where the failure lies. The relation between R and RxR is the same as the relation between R and N. R can be viewed as corresponding so a single cardinal. How many lines you need to construct RxR? The same number as the number of cardinals to construct R.

Every cardinal is either countable or uncountable. Every countable cardinal is either finite or denumerable. There are denumerably many countable cardinals. There are denumerably many finite cardinals. There is only one denumerable cardinal.

That is easy. The hard part I described is PROVING that for an infinite set S and natural number n>0, we have card(S) = card(S^n).

After proving that, cardinal arithmetic is indeed beautifully simple:

If K and L are cardinals, and the larger of them is infinite and the smaller of them is not zero, then

K + L = K * L = max(K L)

The relation between R and RxR is the same as the relation between R and N. — AgentTangarine

That is purely arbitrary unfounded assertion.

On the other hand, in set theory, from rigorously stated axioms, definitions, and rules of inference we prove things.

And I answered a question for you, but you still have not answered my question for you. So the next question for you is: Why do you think one would feel need to answer your questions when you don't answer questions yourself? Wait, I have the answer: Because you are a crank.

Like the interval [0-1]. Uncountable. — AgentTangarine

You contradict yourself. You claim there is a bijection from N onto R, but above you admit that the interval [0 1] is uncountable. And we don't write '[0-1]' to denote and interval.

You are totally mixed up.

And it is beyond me why you think that the stuff you make up in your own head - without rigorous principles and without any understanding of the mathematics you allude to and the terminology you abuse - is somehow true and correct while the mathematics that has been rigorously formulated, studied, scrutinized, critiqued, and checked and thousands of times over rechecked by professionals and students all over the word is all wrong. In other words, what makes a crank tick?

You contradict yourself. You claim there is a bijection from N onto R, but above you admit that the interval [0 1] is uncountable. — TonesInDeepFreeze

You have to read what I write. There are infinite bijections between between N and [0-1]. Like there are an infinite times infinite between N and R. And there are an infinite times infinite between R and RxR.

You have to read what I write. — AgentTangarine

I do. You don't conversely.

There are infinite bijections between between N and [0-1] — AgentTangarine

Read not just what I write, but what is written anywhere you would look: There is no bijection between N and [0 1].

What you wrote is contradictory:

You write that there is a bijection between N and [0 1] and you write that [0 1] is uncountable,

You don't know what you're doing.

That is purely arbitrary unfounded assertion. — TonesInDeepFreeze

If you consider the infinite line the discrete elements on the plane, like the natural numbers on R, than the relation between the lines and RxR, the infinite plane, is conformal to the relation between N and R.

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

You don't know what you're doing — TonesInDeepFreeze

Yeah, that's the zillionth time you mentioned this. I haven't seen one thing to conclude you do. You only make references.

conformal to the relation between N and R. — AgentTangarine

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

You only make references. — AgentTangarine

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

I answered one of your questions. — TonesInDeepFreeze

You haven't answered one!

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

Everyone knows what conformal means.

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

Then what is false?

You haven't answered one! — AgentTangarine

Now you have flat out lied.

how many times you can map N on R
— AgentTangarine

Do you mean N onto R?

The answer is 0. — TonesInDeepFreeze

Again now, your turn to answer my question.

Do you mean N onto R?

The answer is 0. — TonesInDeepFreeze

Ah, I didn't see that one! 0 times? Are you kidding?

Then what is false? — AgentTangarine

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

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

But why false?

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

But why false? — AgentTangarine

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,. — TonesInDeepFreeze

That's no answer why it's false. You seriously believe you can map N zero times on R? What's your question?

Liza is getting tired and reduced to token replies. — TonesInDeepFreeze

Now you take refugee behind empty verbiage. Liza is tired indeed. My wife lies in bed for a couple of hours already... I told her to come too. Three hours ago...

Eliza is now all tangled up in confusion. My answer was to the question about mappings from N onto [0 1] not about why your claim that I have done nothing but give references is false.

I'm not surprised that your attention span wouldn't provide recalling my question: Why won't you look up 'continuum hypothesis' on the Internet?

I'm not surprised that your attention span wouldn't provide recalling my question: Why won't you look up 'continuum hypothesis' on the Internet? — TonesInDeepFreeze

I have done that years ago already. I don't agree though. I'm not a parrot like you.

Now you take refugee behind empty verbiage. — AgentTangarine

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 given references but have posted formulations for you (as I already mentioned I have done that to your PREVIOUS claim that I only give references) and explanations too.

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

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

Then ignore it. The only riddle you gave as an actual answer is that you can map N zero times on R.