Hilbert's Grand Hotel

Hilbert’s Paradox of the Grand Hotel

For those of you who are already familiar with Hilbert’s paradox and want to move straight to the solution and skip my sarcastic nonsense, please click here.

Today I read about Hilbert’s paradox of the Grand Hotel (shame, only today) and I was struck by the illogical human thinking.
That’s right!
Paradoxes are nothing but illogical thinking.

Hilbert’s paradox goes like that:

Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms.[Read the rest in Wikipedia]

When for some stupid reason we create infinite sets, we create them from objects with the same properties. Right?
We can have an infinite set of apples, or an infinite set of shoes, or an infinite set of shoe pairs.
What do we have in Hilbert’s case? (още…)