Terms Commonly Used in Higher Math
CLEARLYI don't want to write down all the "in between" steps.
TRIVIALIf I have to show you how to do this, you're in the wrong class.
OBVIOUSLYI hope you weren't sleeping when we discussed this earlier, because I refuse to repeat it.
RECALLI shouldn't have to tell you this, but for those of you who erase your memory tapes after every test...
WLOG (Without Loss Of Generality)I'm not about to do all the possible cases, so I'll do one and let you figure out the rest.
IT CAN EASILY BE SHOWNEven you, in your finite wisdom, should be able to prove this without me holding your hand.
CHECK or CHECK FOR YOURSELFThis is the boring part of the proof, so you can do it on your own time.
SKETCH OF A PROOFI couldn't verify all the details, so I'll break it down into the parts I couldn't prove.
HINTThe hardest of several possible ways to do a proof.
BRUTE FORCE (AND IGNORANCE)Four special cases, three counting arguments, two long inductions, "and a partridge in a pair tree."
SOFT PROOFOne third less filling (of the page) than your regular proof, but it requires two extra years of course work just to understand the terms.
ELEGANT PROOFRequires no previous knowledge of the subject matter and is less than ten lines long.
SIMILARLYAt least one line of the proof of this case is the same as before.
CANONICAL FORM4 out of 5 mathematicians surveyed recommended this as the final form for their students who choose to finish.
TFAE (The Following Are Equivalent)If I say this it means that, and if I say that it means the other thing, and if I say the other thing...
BY A PREVIOUS THEOREMI don't remember how it goes (come to think of it I'm not really sure we did this at all), but if I stated it right (or at all), then the rest of this follows.
TWO LINE PROOFI'll leave out everything but the conclusion, you can't question 'em if you can't see 'em.
BRIEFLYI'm running out of time, so I'll just write and talk faster.
LET'S TALK THROUGH ITI don't want to write it on the board lest I make a mistake.
PROCEED FORMALLYManipulate symbols by the rules without any hint of their true meaning (popular in pure math courses).
QUANTIFYI can't find anything wrong with your proof except that it won't work if x is a moon of Jupiter (Popular in applied math courses).
PROOF OMITTEDTrust me, It's true.