At some lectures I attended perhaps 50 years ago, there was a discussion about infinities.
Am I the only person to remember all this?

The size of a countable set, was defined as “Aleph null" א subscript 0
The smallest infinity.
Because the Hebrew script is to difficult to handle in Word, I shall call it N.
The arithmetic if these infinite numbers is interesting.
If N is the size of the non-negative integers, {0,1,2,3,4,5 ...)
then, for example the set of positive and negative integers {0,+1,-1,+2,-2,+3,-3,…} is of size 2N.
and the set of positive even numbers {0,2,4,6,…} is of size ½ N.
So, in infinite arithmetic (N being Aleph Null)
N + 1 = N
N x 2 = N

then fractions, which can be defined as the ration of two integers a/b
are therefore a set of size N squared
and so
N x N (= N squared) = N

Can we find a larger number? Answer, yes.

If we move on to Real numbers, rather than rationals,
we find the set is uncountable. (Bigger than countables)
So writing the real numbers as a countably infinite decimal expansion for example,
the real number set is of size 10 tot he power N
A countable set of choices of digit.
So 2 to the power N (= 10 to the power N, etc) is bigger. We would call it Aleph 1.

I never pursued this any further.
But can we construct even bigger infinities?
Is there an Aleph 2 and an Aleph 3, even an Aleph aleph.

This is infinitely better than Googleplex!

Is there any literature that takes this further?
I would be glad to know.

Or is all this in Georg Cantor's work?

Meanwhile back to the real world (or rational ...)

Richard Billinghurst. St John's 1967. Mathematics. later theology. It is all the same! God is a mathematician.