Answer:
Definition:
An integer is a number that can be written without a fractional component. They can be positive, negative, or zero.
Explanation:

In order to prove that (n/k) * (k/r) = (n/r) * ((n-r)/(n-r)) for all integers n, k, and r with n ≥ k ≥ r, we can follow these steps:
- Simplify both sides of the equation.
- Use the fact that n ≥ k ≥ r to show that both sides are equal.
Let's proceed with the proof:
Simplify both sides of the equation.
Left-hand side (LHS):
(n/k) * (k/r)
Multiply the fractions:
LHS = (n * k) / (k * r) we can cancel out k.
LHS = n/r
Right-hand side (RHS):
(n/r) * ((n-r)/(n-r))
The (n-r) terms in the numerator and denominator of the RHS cancel out:
RHS = (n/r) * (1)
RHS = n/r
Use the fact that n ≥ k ≥ r to show that both sides are equal.
Since n ≥ k and k ≥ r, we can conclude that n ≥ r.
Thus, (n-r) is a non-negative integer, as (n-r) is the difference between two integers (n and r), and the result will always be an integer.
Hence Proved: