or an arrowhead pointing to the right (>). When you use this symbol, remember that “larger”
means “more positive” or “less negative.”
- To state that 3 is strictly larger than −7/2, write 3 >−7/2.
- To state or require that x is strictly larger than 0, write x> 0.
- To state or require that x is strictly larger than y, write x>y.
- To state or require that 2x is strictly larger than x, write 2x>x.
Strictly smaller
When a certain quantity is always smaller than (or less than) some other quantity, the “strictly
smaller than” symbol is used. It looks like a letter V rotated a quarter-turn clockwise, or an
arrowhead pointing to the left (<). When you use this symbol, remember that “smaller” means
“less positive” or “more negative.”
- To state that −1 is strictly smaller than 7/2, write − 1 < 7/2.
- To state or require that x is strictly smaller than 0, write x< 0.
- To state or require that x is strictly smaller than y, write x<y.
- To state or require that 2x is strictly smaller than x, write 2x<x.
Larger than or equal
When a certain quantity is always larger than or equal to some other quantity, the “larger than
or equal” symbol is used. It looks like a Roman numeral IV rotated a quarter-turn counter-
clockwise, or an arrowhead pointing to the right with a line underneath (≥).
- To state that 3 is larger than or equal to −7/2, write 3 ≥−7/2.
- To state or require that x is larger than or equal to 0, write x≥ 0.
- To state or require that x is larger than or equal to y, write x≥y.
- To state or require that 2x is larger than or equal to x, write 2x≥x.
Smaller than or equal
When a certain quantity is always smaller than or equal to some other quantity, the “smaller
than or equal” symbol is used. It looks like a Roman numeral VI rotated a quarter-turn clock-
wise, or an arrowhead pointing to the left with a line underneath (≤).
- To state that −1 is smaller than or equal to 7/2, write − 1 ≤−7/2.
- To state or require that x is smaller than or equal to 0, write x≤ 0.
- To state or require that x is smaller than or equal to y, writex≤y.
- To state or require that 2x is smaller than or equal to x, write 2x≤x.
Are you confused?
How can a quantity 2x can be strictly smaller than x, or smaller than or equal to x, as is mentioned twice
in the above examples? Think for a moment about the meaning of “smaller” with respect to positive and
negative numbers. Then remember what happens when you multiply a negative number by a positive
Inequalities 177