Le 19/07/2013 20:54, Nekar Xenos nous fit lire :
> I don't know.
> 
> Maybe I should start with something simpler.
> 
> Infinity + Infinity = ?
> 
> Is there any other answer than 2(Infinity)?

Well, if anything else, that's never the answer.

Infinity + Infinity = Infinity.

> 
> If so please explain.

You have to be aware that some Infinity are bigger than some other
Infinity. (rahh... not now!)

To ease the understanding, the smallest infinity is called Aleph-0.
(well, that still a controversial subject, linked to the Axiom of Choice)

The natural integer (0, 1, 2, .. and so on) are in the N set, whose
cardinality is indeed Aleph-0.

Imagine one hotel of infinite room, each room numbered uniquely from N
set. And now you build another one next to it, of same size.
You then renumber the room of the first hotel x--> 2x, and of the second
hotel y--> 2y+1. You now have a single hotel-company of the same size as
one of the original.

You can also split it in multiple (finite number) hotels, all of
infinite size... they were already there!

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