Inequality is when one object is:

• Smaller than the other (\displaystyle{ a\lt b } means that a is smaller than b)
• Bigger than the other (\displaystyle{ a\gt b } means that a is bigger than b)
• Not smaller than the other (\displaystyle{ a\geq b } means that a is not smaller than b, that is, it is either bigger, or equal to b)
• Not bigger than the other (\displaystyle{ a\leq b } means that a is not bigger than b, or it is smaller or equal to b)

Inequality is sometimes used to name a statement that one expression is smaller, greater, not smaller or not greater than the other.