Describe to a layman the paradox of the hotel infinity

What is a googol, googolplex and Graham’s number?
What is infinity?
What ‘size’ of infinity are the counting numbers, prime numbers, odd numbers, and rational numbers (fractions)?
Describe to a layman the paradox of the hotel infinity
What do you get when you add something (be it finite or infinite) to infinity?
What do you get when you subtract something (be it finite or infinite) from infinity? Do you always get a single answer and if not why?
How was the ‘next level’ of infinity discovered?
How can mathematics function if we do not allow the concept of infinity to exist?
What led to the mental breakdown of the mathematician Cantor?
If we allow a monkey to type at random for an infinite amount of time, what can they produce?
Is the universe finite or infinite?
How can we compute the distance that we would need to travel in order to find another copy of ourselves? If so, what does this number look like?

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