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• The concepts for this exercise are summarized below.
  For a complete discussion, read the text (and solutions are here).

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 ‘[beautiful math coming... please be patient]$\,>\,$’ (greater than) and ‘[beautiful math coming... please be patient]$\,<\,$’ (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   [beautiful math coming... please be patient] $\,a > b\,$   is read aloud as “$\,a\,$ is greater than $\,b\,$”.
The sentence   [beautiful math coming... please be patient]$\,a > b\,$   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   [beautiful math coming... please be patient] $\,a < b\,$   is read aloud as “$\,a\,$ is less than $\,b\,$”.
The sentence   [beautiful math coming... please be patient]$\,a < b\,$   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.