Is (-4) over 0 rational

Answer 1

Brief answer: yes.

Detailed answer:

First, the definition of an rational number. Given any two ordered pair of integers (m,n), (p,q) with n,q !=0, define a relation (m,n)~(p,q) if and only if mq =np over the integers. The equivalence class of (m,n), denoted [m,n] defined as {(p,q):(p,q)~(m,n)}. Then the set of all equivalence classes is the rational numbers Q:={[m,n]:m,n are integers, n not equal to 0}. And the relation ~ over pairs of integers becomes = as [m,n]=[p,q] if and only if (m,n) ~ (p,q).

But the notation [m,n] is too ugly, so we write it as m/n instead. Read m over n, or m divided by n, now we have division defined as well.

Now consider if we create a map f that sends integers into the rationals. f(k) = [k,1] for all integer k, we claim this is a good way of "inscribing" integers into the rationals. That is for every k, there is one and only one class [k,1], this is easy. And for every class of the form [b,1], we can find integer b that maps to it.

Now if we just imagine that [k,1] is actually just k, then here we go, integers are "in" rational numbers too!

-1763 is an integer.

Answer 2

Not Rational (-4)/0

A rational number is any integer fraction terminating decimal or repeating decimal