The middle of the road

I've proposed several times in this blog that we consider math to be a language of counting, measurement, shapes and calculation; a language with precise definitions and specialized terms.

I'd like to adjust my definition to include the concept of comparison. Math provides us with the means to compare and evaluate the world around us.

While there are subtleties which require us to use a wide range of comparison terms, the simplest comparisons could be narrowed down to two choices.

• This object is the same as that one.
• This object is not the same.

A much more satisfactory comparison can be made using three terms. In essence, we are still using the single comparison as well, but we are leaving that comparison unspoken.

• This object is the same as that one
• This object is better than that one (therefore it is not the same)
• This object is not as nice as that one (thus it too is not the same)

Kindergarten Excel Math starts off not with numbers, but with comparison words that a 5-year-old person could use. The table below contains a variety of these sets of words used by English-speaking people of all ages. I invite you to think of more terms:

Minus	Equals	Plus
less than	equal to	greater than
lower	same height	higher
below	same height	above
shorter	same height	taller
shorter	same length	longer
narrower	same width	wider
under	middle	over
bottom	middle	top
left	middle	right
thinner	same thickness	thicker
inside	on the line	outside
off	midway	on
before	during	after
fewer	same	more
fewest	same	most
least	same	most
different	similar	identical
front	middle	back
forward	not moving	backward
in front of	aligned with	behind
younger	same age	older

This concludes my list of comparison terms. But before I leave, here's a gift for those who insist on numbers in every math blog. Your assignment? Describe the relative positions of these three numbers using at least 3 sets of comparative terms from the table above: