Question

Find the sum of all the decimal numbers which
lie between 2 and 5, and
the numbers should have only digits 3, 4, 6 and 8 occurring exactly once, but have no other digits.

Answer 1

Answer:

The cardinality of the set of numbers strictly between 2 and 3 is:

Zero for Natural numbers

One for whole multiples of 12

Two for whole multiples of 47

ℵ0 for Rational numbers

ℵ0 for Algebraic numbers

ℵ0 for Constructible numbers

c=2ℵ0 for Real numbers

And there are unsetly many Surreal numbers because there are “too many” to fit in a set. In fact there are unsetly many Surreal numbers between any two distinct Real numbers nomatter how close they are to each other!

As you can see you might need to define “number” a little more precisely for there to be a simple answer to your question. You might also note that the simple answer “infinity” is not as simple as you might think.