without loss of generality. ``I'm only going to show you part of the proof because the rest is exactly the same.''
such that.
quod erat demonstrandum (``which was to be proved''). Marks the end of a proof. Nowadays, textbooks and scholarly papers often use a small black square instead. Maths majors and graduate students, on the other hand, usually mark the end of their proofs by drinking heavily and passing out slumped over the paper or keyboard. Kids, don't try this at home.
ce qu'il fallait démontrer. French for QED.
with respect to.
the following are equivalent. Proceeds a list of logical statements which are claimed or proved to be logically equivalent to one another.
then a miracle occurs. ``I have no idea how to finish this proof.'' Usually found in answers to exam problems.
it can be shown. The more respectable form of `TAMO'. Unlike TAMO, this one appears in serious mathematical writing.
well-formed formula. In logic, formal systems, and such.
almost everywhere. In contexts where a measure mu is defined on a space X, a property P(x) holds almost everywhere on X if the set of points n of X for which P(n) does not hold has mu-measure zero. Also we say P(x) for a.a. x in X, standing for almost all x in X.

Sometimes almost everywhere is used in topological spaces where no measure is defined; in this context it usually means that a property holds for all points except for a set of first category, that is, except for a countable union of nowhere dense sets. However it is more common in this case to say that the property holds residually (a residual set being the complement of a set of first category).

Sometimes you see the French version p.p. (for presque partout).

Log in or register to write something here or to contact authors.