Why we use a ‘less than sign’ and not a ‘fewer than sign’

English is a difficult language to master because it has many rules. Take “less” and “fewer,” for example. Both words mean that a quantity is diminished in size, but they are not interchangeable if used correctly. Use “less” when you are referring to a quantity that cannot be counted and “fewer” when you can count the quantity. For example, you cannot count “light.” You say, “I have less light.” You can count “light bulbs,” however, so you say, “I have fewer light bulbs.”

So why does mathematics have a less than sign rather than a fewer than sign? We’re counting quantities in math, right?

The answer comes from several directions: the current state of the English language, history, and the idea of something being “English-like.”

In English, there are exceptions to the count rule, says grammar.quickanddirtytips.com. Quoting the venerable Fowler’s Modern English Usage and dictionary.com, the website says, “for example, it is customary to use the word “less” to describe time, money, and distance. For example, you could say, ‘That wedding reception lasted less than two hours. I hope they paid the band less than $400.’ So keep in mind that time, money, and distance are different, but if you stick with the quick and dirty tip that less is for mass nouns and fewer is for count nouns, you’ll be right most of the time.”

Another explanation comes from history itself. The English language fought over “less” and “fewer.” Blogger Mark Israel (alt-usage-english.org/excerpts/fxlessvs.html says:

The rule usually encountered is: use “fewer” for things you count (individually), and “less” for things you measure:  “fewer apples”, “less water”.  Since “less” is also used as an adverb
(“less successful”), “fewer” helps to distinguish “fewer successful professionals” (fewer professionals who are successful) from “less successful professionals” (professionals who are less successful).
(No such distinction is possible with “more”, which serves as the antonym of both “less” and “fewer”.) “Less” has been used in the sense of “fewer” since the time of
King Alfred the Great (9th century), and is still common in that sense, especially informally in the U.S.; but in British English it became so rare that the 1st edition of the [Oxford English Dictionary]
(in a section prepared in 1902) gave no citation more recent than 1579 and gave the usage label “Now regarded as incorrect.”  The 2nd edition of the OED added two 19th-century citations, and changed the usage label to
“Frequently found but generally regarded as incorrect.”

With all of this confusion, is it no wonder that the less than sign first appeared in the book Algebraicas Resolvendas, by Thomas Harriot (1560-1621), published posthumously in 1631. If English was going to fight, mathematics picked a name and stuck with it. You could say, then, that the language of mathematics is “English-like.” A modern example are computer languages, such as COBOL. COBOL isn’t really Engish. Examine this COBOL syntax and notice its exactness:

MOVE Source$#il TO Destination$#i …

“MOVE” and “TO” look like English, but those words must be used according to COBOL rules, not English rules. A compiler wouldn’t know what to do with a statement “MOVE THIS OVER THERE”: “THIS” Would have to be declared a source and “THERE” a destination, but “OVER” has no meaning in this statement.

Mathematics is also its own language. Yes, we’ve all seen “word problems” since grade school, but the intent isn’t to pretty up the English language. The intent is to construct a mathematical equation — derived from the English (another language would obviously do as well) — to solve the problem. Here’s a very simple problem:

The price of a computer is less than $2000, the price of a printer is less than $300, and the price of a scanner is less than $200. What is the total estimated cost of the three items?

Here we took from English the information to construct what we need to get our answer. We’re not interested in good grammar, bad grammar, or whether “less” came before “fewer.”  We want an answer, and we have it, and we use the name the symbol has had for some 450 years.

Of course, when we write English, we’ll use  “fewer” and “less” according to current rules: Whwn we can count what we’re writing about, we’ll use “fewer”; “we’ll make fewer mistakes.” When we can’t count the quantity, we’ll use “less”;  ”we want less malarky.”

Where to find more information:

• Burchfield, R. W, ed. The New Fowler’s Modern English Usage. Third edition. New York: Oxford, 1996, p. 295.
• few. Dictionary.com. The American Heritage® Dictionary of the English Language, Fourth Edition. Boston: Houghton Mifflin Company, 2004. http://dictionary.reference.com/browse/few (accessed: May 10, 2007).
• grammar.quickanddirtytips.com/less-versus-fewer.aspx
• cobolprog.blogspot.com/2008/07/move-command.html
• www.onlinemathlearning.com/math-word-problems.html
• alt-usage-english.org/excerpts/fxlessvs.html