negation of inequality

In sec 3.1, i understand negations and what not but givung the negation for inequalities confuses me a little bit. I understand what to do but the sybols are what is tripping me up.

a < b means that a is less than b. The negation of this statement has to include every possibility that would make this statement false.

a < b is false if a is greater than b. It is also false if a is equal to b. So the negation would be a >= b, where >= is the 'greater-than-or-equal' sign.

By similar reasoning:

The negation of a <= b would be a > b. The negation of a >= b would be a < b. The negation of a > b would be a <= b.