Countably infinite set

>real numbers
>not real
how can something that is real also not be real?

Not true. There's simply a subset of the real numbers that go by the same names as natural numbers.

If two sets are both unique and identical then they're the same set

Identical sets are by definition unique, so yes. I guess he could've been more clear and said
>Give me a natural number and I give you its successor
>Give me a non-natural real number and I can not

But what he meant was clear from context, so this entire argument is dumb.

0.99999...

Is our perception real?

So in other words they're real numbers. Got it

You can basically count on both sides, either (n+1)/q or n/(q+1).

"Countable" is vague. You can count parts of an infinite set, but you can't complete the synthesis, that's what makes it infinite.

Finding a bijection between the elements of some set and the natural numbers is literally counting them so the terminology is instructive.

>e.g. there is a row of shoes, we count them by successively assigning natural numbers to them.

A mathematics major would have some quip explaining how infinity is but at the end of the day, he will hust be one more retard in a sea of retards called mathlets who only vaguely pretend to understand definitions of infinity, meanwhile being unable to produce an example of infinity being used towards solution of any real world problem.

It's really not a maths concept at all. Mathlets assume otherwise.

Don't take math too seriously, it's mostly just bullshit.

>the set of natural numbers includes ALL natural numbers
>the last natural number is a number
>the set of natural numbers does not contain the last natural number

@9624656
@9624958
retards

There is no "last natural number", or "greatest natural number". This is why the set is said to be infinite, i.e. not finite.

@9625356

Retard learn how to use Veeky Forums

He thinks (You)'s are upvotes

go back to your redit faggots

Countably infinite = graduated.

how can numbers be real if our eyes aren't real

Absolute mongoloid.

=1

>meanwhile being unable to produce an example of infinity being used towards solution of any real world problem.
On the top of my head I can name dozens of examples where infinity and concepts developed with infinity are used in real world problems.

Do you honestly think that Engineering would work without "infinite sums".
Have you even taken *any* engineering class and seen where these mathematical concepts are used literally everywhere?