Question

Let α and β be two real numbers so that α ≤ β and β ≤ α. Then α = β.

Prove.

Answer 1

Inequality describes a relationship between two different values.

The notation a<b means that a is strictly smaller in size than b, while the notation a>b means that 

a is strictly greater than b.

The notion a≤b means that a is less than or equal to b, while the notation a≥b means that a is greater than or equal to b.

In this question a≤b and a≥b. It follows that, a can not be greater and less than b. So, a will be equal to b:

                        a=b;