Question

How many whole numbers are there between 0 and 1?

Answer 1

None

Explanation:

First we need a few definitions:

(i) Your interval is defined by `(0,1)` on the real line
That is any number `x` where `0 < x <1`

(ii) Whole numbers are integers,

By definition intergers are: any of the natural numbers, the negatives of these numbers, or zero, That is any number `x in ZZ`

From the definition of integers, no number `x` can satisfy both (i) and (ii) above.

Hence, there are no whole numbers between 0 and 1.

NB: There are in fact an infinite number of real numbers in the interval `(0,1)`. These consist of the rational numbers which can be represented by `p/q {p,q} in ZZ: q!=0` (such as `1/2`) and irrational numbers which cannot be represented by `p/q {p,q} in ZZ: q!=0` (such as `1/sqrt2`).