Various glitches to watch for, when you're trying to be precise...
I was playing a game with some friends, and we came across the rule:
If you have more cards than any other player, then discard a card.Does this mean "than all other players", or "than some other player"? Our group's opinion was divided (incl. across many native English speakers).
In our terms of first-order logic, it's not always clear whether "any" means for-all, or for-some (there-exists). Or perhpas more accurately, in the phrase "for any x", is x required to be arbitrary?
[Linguistics students, or those who are so sure the rule clearly intended "than all other players": Compare with
"If any other player has fewer points than you, ..."We're just switching "you > any-other" to "any-other < you". Admittedly this changes things from an active voice to a passive voice (I think that's what I'm doing at least), but otherwise sure seems like it should be an equivalent statement. Yet, it suddenly reverses most people's opinion on the meaning of "any". ]
In your proof-writing (and your English writing, and your informal writing), think about replacing "any" with either "every" or with "some", to make your meaning clear.
In proofs, slipping in the word "the" suggests both existence and uniqueness: "The first postive real number" (which doesn't exist), or "the fastest time" (which may not be unique). Just be aware when introducing the word,
Use "last" if you mean "last", and "previous" if you mean "previous". In particular, in programs which iterate through a list, a variable that refers to the previous item visited shouldn't be named last, though people do this all the time. And my company's multi-million dollar phone system has a button "Last Message", which really just takes you to the previous message; there is no way to jump directly to the last message, sigh.