# Dictionary of Definitions of Terms Used in Math Lectures

CLEARLY:
I don’t want to write down all the “in-between” steps.
TRIVIAL:
If I have to show you how to do this, you’re in the wrong class.
OBVIOUSLY:
I hope you weren’t sleeping when we discussed this earlier because I refuse to repeat it.
RECALL:
I 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 SHOWN:
Even you, in your finite wisdom, should be able to prove this without me holding your hand.
CHECK or CHECK FOR YOURSELF:
This is the boring part of the proof, so you can do it on your own time.
SKETCH OF A PROOF:
I couldn’t verify all the details, so I’ll break it down into the parts I couldn’t prove.
HINT:
The hardest of several possible ways to do a proof.
BRUTE FORCE:
Four special cases, three counting arguments, two long inductions, “and a partridge in a pear tree.”
SOFT PROOF:

One 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 PROOF:
Requires no previous knowledge of the subject matter and is less than ten lines long.
SIMILARLY:
At least one line of the proof of this case is the same as before.
CANONICAL FORM:
4 out of 5 mathematicians surveyed recommended this as the final form for their students who choose to finish.
TFA (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 THEOREM:

I 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 PROOF:
I’ll leave out everything but the conclusion, you can’t question ’em if you can’t see ’em.
BRIEFLY:
I’m running out of time, so I’ll just write and talk faster.
LET’S TALK THROUGH IT:
I don’t want to write it on the board lest I make a mistake.
PROCEED FORMALLY:
Manipulate symbols by the rules without any hint of their true meaning (popular in pure math courses).
QUANTIFY:
I can’t find anything wrong with your proof except that it won’t work if x is a moon of Jupiter.
PROOF OMITTED:
Trust me, It’s true.