Magnus Anderson

It's a subtle point that is difficult to explain. Perhaps I should have used "any" instead of "every" in that second quote of mine. Let me try to expl...

The onus of proof is always on the one making the claim. If you're making the claim that bijection between N and N0 exists, you have to show it, and t...

You very clearly don't understand how language, definitions and oxymorons work. Square-circles aren't squares either. They are also not circles. But t...

The difference is that bijection means that you can take every element from N -- not merely any arbitrary subset of it -- and uniquely pair it with an...

And remember, the onus of proof is always on the one making the claim. You can't claim that bijection exists between N and N0 merely because you can t...

Not really. And that's a commonly made mistake. Bijection does not mean that you can take ANY element from N and uniquely pair it with an element from...

Let me illustrate my point. Functions can be malformed. They can contain internal contradictions that effectively render them as non-existent. Conside...

You would have to prove that. I am, however, pretty sure you can't do it. But I can show, as I already did, that YOUR reasoning is circular. So what y...

You can't do that. Logic prohibits it. There are more "labels" in N0 than there are in N. And you're relying on a deceptive "proof". You think that, j...

The symbol we're talking about is this: f: N -> N0, f( n ) = n - 1 The definition of a symbol specifies what that symbol can be used to represent -- h...

Another lie. It's not only you. I am aware of that. Your confidence is entirely grounded in what someone else said.

Only a completely blind person can see any trace of finitism in what I'm saying.

That's a lie you've been shamelessly pushing forward. The definition does not apply only to finite sets. It applies to all sets. The only reason you t...

There's no need to list all of the elements. All this talk about constructivism, intuitionism and finitism misses the point ( I do not subscribe to an...

I can't quote the entire part, the LaTeX code gets messed up for some reason. You are right that f( n ) = n ? 1 by itself is not a complete definition...

Not N0 but f(n) = n - 1. That function is a bijection by definition. Yes. It is not explicitly stated in the definition. However, the definition impli...

It is defined as a bijection. The same way square-circles are defined as shapes that are both circles and squares. That does not mean they are logical...

You're not responding to what's in the quote. You did not prove the following: that just because you can think of a function that is defined as biject...

Bullshit. You're literally copy-pasting textbook arguments. Zero thinking on your part.

Not really. Banno's argument is flawed because it is based on the erroneous premise that I already covered: "If we can think of a function that is def...

They don't. It's called ad hoc rationalization.

I appreciate your response but I disagree with your conclusion, namely, that we're using two different definitions of the term "same size". I am quite...

You're missing the point. What has to be shown is that the fact that one can think of f(n) = n - 1 means that there exists one-to-one correspondence, ...

For a grownup man, that's a pretty childish response. If the word "function" is defined the way mathematicians define it, namely, as a relation betwee...

"Making shit up" is what people confuse with thinking when they know nothing other than to read books and / or be sycophants. In your case, it's obvio...

That's a pretty bad excuse. The dispute was over the definition of the word "infinity". You were supposed to provide a definition that is different fr...

And you really should take my advice and use your brain for once. Reading isn't thinking.

Bravo! Yikes. That goes against what Cantor said. And I am pretty sure you won't be able to prove it ( asserting it isn't a proof. ) You're very clear...

What you provided is the definition of the countable infinity. That's not the same as infinity. Furthermore, the provided definition does not contradi...

If you're going to take pride in your book reading skills, even though we're on a forum that is supposedly about thinking and not reading, at least do...

Here's another way one can explain why "Which one is left out?" question is problematic. Let A be a finite set that is { 1, 2, 3, ..., 100 }. Let B be...

And adding four to an integer is still an integer. The resulting category is the same. If you add four to a number that is larger than every integer, ...

Not quite. Definitions are prior. Nothing can invalidate them. If "add" means "increase in size", nothing can make it change its meaning. And the word...

I can't think instead of you, Banno. If you can't do it, that's fine. But don't make it look like it's the other person's problem. By definition, to a...

Silly question. The point is that you can't put them into one-to-one correspondence. In other words, one element must be left unpaired. Which one? You...

And there are not enough elements in the set A = { 1/2, 1/3, 1/4, ... } to put it into one-to-one correspondence with the set of natural numbers N = {...

Why not? If you can take Cantor's, you can take mine. You didn't do that. You merely asserted that you did it. I can do the same for finite sets. Cons...

That's not true.

Hi @"Tristan L", If the discovery-process is deterministic, the discovered solution will necessarily be a solution that existed in a number of spaces ...

@"Pffhorest" Creativity is simply the ability to discover previously undisocvered solutions to problems. How you're going to discover such solutions i...

But love, courage and joy are neither greater than nor less than any sort of number.

I'd say anything that can be said to be greater than or less than something else is a quantity (and therefore a number.) Infinity > every integer. The...

Depends on whether we're talking about infinity in the general sense of the word (as in, any number greater than every integer) or in the specific sen...

Infinity is a number greater than every integer. And infinity + 1 = infinity is true only in the sense that if you take an infinite number and add one...

Thank you very much.

As you say, an infinite sum may not have a limit. If you say that the concept of infinite sum and the concept of limit are one and the same concept th...

I avoid the "..." notation because it looks ugly when used in forums without LaTeX support. But yes, that's what I mean. "0.333~" represents the infin...

This depends on the meaning of the symbol "0.333~". According to the way most people define "0.333~", it is not true that "1/3 = 0.333~". By standard ...

I do not understand why you think that things that exist in space and/or time must have size. Why is it impossible for something to exist (in space an...

I am not sure why you think so, Points do exist (both in time and space.) Consider that at any point in time, you occupy certain point in space. So th...