Question

Prove by contradiction that a real number that is less than every positive real number cannot be positive

Answer 1

assume that there is a real number less than every positive real number

Answer 2

and that real number is positive

Answer 3

now for the actual hard part where you figure out how to prove that that is contradictory

Answer 4

then say that number is a. But a is a positive real number, so there must be a positive real number less than a, which is a contradiction from the original statement.