Let A set of real numbers Let B set of integers f is a rel

Let A = set of real numbers. Let B = set of integers. f is a relation from A to B defined as f(a) = “the greatest integer less than or equal to a”. Is f a function? Please explain your answer.

Solution

For a relation to be a function we require that:

For each x in A ,f(x) must be unique

We know for any real number there is a unique integer ,n so that:

n<=x<n+1

n is the greatest integer less than or equal to x

So,

f(x)=n which is unique.

Hence, f is a function.