how do you prove that infinity actually exist? how do you prove that infinity actually exist? @Mathematics

Question

anonymous · Answer

You can't prove it. But everyone knows that numbers are endless. If you know them, you can keep counting and never stop.

anonymous · Answer

If you write a hundred digit number, it is still a number. Since we cannot count up to such big numbers, we have named the largest infinity. There is no fixed value of infinity.

anonymous · Answer

This is enough proof, right?

sasogeek · Answer

it makes sense, not sure how much of a proof it is though. one of those things u just have to accept by faith

anonymous · Answer

I guess so.

amistre64 · Answer

i spose it depends on your definition of infinity.

numerical, philisophical, time, space, etc ...

anonymous · Answer

The answer depends on the entity you are talking 
about. In mathematics, we deal only with abstract entities like the 
whole numbers or integers, and by definition those are infinite, just 
because there is nothing in our definitions that makes them stop. This 
doesn't mean that all of the infinitely many possible numbers can ever 
be used; on the contrary, it says that no one can ever use up all the 
numbers, even if time does go on forever.

alfie · Answer

$$\forall \!\, n \in N n < n+1$$

For induction, let's try with P1

n < n+1
1 < 2
That's true, so for.

n < n+1 TRUE
We have to find
n+1 < n+2 TRUE.

But this is obvious, since:

n < n + 1
We add "+1" to both members getting

n+1 < n + 2 Which is what we wanted to prove.

$$\forall \!\, n \in N $$

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I just came out with this, but I guess it should be right >.<