In several recent AlgPoW problems there have been occasions where students have used the word "amount" incorrectly. As in a problem about a number of soldiers marching... Of course, they said "...amount of soldiers...".
It's a matter of countable vs uncountable nouns. So I decided it was time to "go public" and explain the matter directly. Therefore I wrote about this for my solvers in my Tip of the Week feature. Here is what I said:
------------------- Two words that mean different things in math are: number and amount. They are often used incorrectly in common speech and no one seems to mind. But we should be more careful when we write them in PoW explanations.
It's really quite simple to know. If you can "count" the items referred to, use "number." A recent problem involved the "number of soldiers" that were marching. To say the "amount of soldiers" sounds a bit strange to the ear.
The word "amount," therefore, is used when you can't count, as in the "amount of milk in a glass." Of course, you could count the "number of glasses of milk" or the "number of fluid ounces in the glass," but that's different. You're counting glasses, not the milk itself.
I have now just created a sequel to that, for "less" and "fewer". It says:
------------------------ Two ÂTipsÂ ago, I explained the words "amount" and "number" This time weÂll look at two words often used with them when we compare things: less and fewer.
When we are comparing countable things, using number, we should say "fewer". Example: "There are fewer cookies on my plate than on yours." [Do NOT say: "Â less cookiesÂ ".]
On the other hand, use "less" when "amount" is involved. Example: "There is less milk in my glass after I drank some of it."
However, you might use "fewer" with milk if you're counting glasses of milk. Look: "There are fewer glasses of milk on this table than on that one." That's because we're counting the number of glasses, not the amount of the milk.