Question

Show the conjecture is false by finding a counterexample.

m If m does not equal -1, then < 1.

Answer 1

Dividing any positive number m over (m+1) leads to a positive result that is smaller than one. This is because the denominator is larger than the numerator.

However, if m is negative, then it's a different story. Consider m = -2

If m = -2, then m+1 = -2+1 = -1

Meaning that
`(m)/(m+1) = (-2)/(-1) = 2` but this result is not less than 1

So m = -2 is one counterexample of infinitely many to show that
`(m)/(m+1) < 1, \text{ with } m \\e -1` is not always true. If you restricted m to be positive, then the inequality would be true.