Wednesday, January 14, 2009

Definitions of Terms Commonly Used in Math

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, here it is again.

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.

ONE MAY SHOW: One did, his name was Gauss.

IT IS WELL KNOWN: See "Mathematische Zeitschrift'', vol XXXVI, 1892.

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 the details, so I'll break it down into 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 pair 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, 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 the answer.

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, then the rest of this follows.

TWO LINE PROOF: I'll leave out everything but the conclusion.

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 because I'll make a mistake.

PROCEED FORMALLY: Manipulate symbols by the rules without any hint of their true meaning.

QUANTIFY: I can't find anything wrong with your proof except that it won't work if x is 0.

FINALLY: Only ten more steps to go...

Q.E.D. : T.G.I.F.

PROOF OMITTED: Trust me, it's true.

Here is the source.

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