Question

Question #9644a

Answer 1

There are no integer numbers between `89` and `90`
but there are infinitely many rational (or real) numbers in this range.

Explanation:

Between `89` and `90`
we have
`color(white)("XXX")88 1/2`
`color(white)("XXX")89 1/3, 89 2/3`
`color(white)("XXX")89 1/4, 89 3/4`
`color(white)("XXX")89 1/5, 89 2/5, 89 3/5, 89 4/5`
and so on....

Answer 2

Depends

Explanation:

It depends if you are taking the numbers only till integers, which range from `-oo ... 0 ... +oo`, they only take numbers which are not fractional, or have decimals,
For example, 12,-3,45,154,-63252 are integers, `1/2,5/3,5 9/12` are not integers, they go to rational numbers.

So,
If you take only integers, there are no numbers b/w 89 and 90,
But if you take rational numbers, there are infinite numbers of numbers b/w 89 and 90
For example,
`268/3,269/3,446/5,449/5`
The more you increase the denominators, the more numbers come in b/w