# Bigger, Smaller, Greater, Lesser

There are different words that can be used to compare real numbers: bigger, smaller, greater, lesser.

Bigger and greater do NOT mean the same thing! Smaller and lesser do NOT mean the same thing!

Bigger and smaller have to do with distance from zero. Thus, the words big and small are used to compare the sizes (absolute value) of numbers.

Greater and lesser have to do with left/right positioning. The verbs ‘$\, \gt \,$’ (greater than) and ‘$\, \lt \,$’ (less than) are used to talk about this left/right ordering.

Bigger means farther away from zero. Smaller means closer to zero.

Greater means farther to the right on a number line. The sentence   $\,a \gt b\,$   is read aloud as ‘$\,a\,$ is greater than $\,b\,$’. The sentence   $\,a \gt b\,$   is true precisely when $\,a\,$ lies to the right of $\,b\,$ on a number line.

Lesser (or less than) means farther to the left on a number line. The sentence   $\,a \lt b\,$   is read aloud as ‘$\,a\,$ is less than $\,b\,$’. The sentence   $\,a \lt b\,$   is true precisely when $\,a\,$ lies to the left of $\,b\,$ on a number line.

## Memory Devices

• The words Lesser, Less than, and Least all begin with the letter ‘L and all have to do with lying to the Left on a number line.
• The word greateR ends with the letter ‘R and has to do with lying to the Right on a number line.

## Examples

Question: Compare the numbers $\,-10\,$ and $\,7\,.$ Which is bigger? Why?
Solution: The number $\,-10\,$ is bigger, because it is farther away from zero.
Question: Compare the numbers $\,-10\,$ and $\,7\,.$ Which is greater? Why?
Solution: The number $\,7\,$ is greater, because it is farther to the right on a number line.
Question: Compare the numbers $\,-10\,$ and $\,7\,.$ Which is smaller? Why?
Solution: The number $\,7\,$ is smaller, because it is closer to zero.
Question: Compare the numbers $\,-10\,$ and $\,7\,.$ Which is lesser? Why?
Solution: The number $\,-10\,$ is lesser, because it is farther to the left on a number line.