General mathematical vocabulary

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PhraseDefinition
a priori A fact is known 'a priori' if it is evident from logic alone, without need of evidence.
ad hoc For this purpose
ad infinitum To infinity, usually referring to a never ending process.
Ansatz An educated guess that is not rigourously backed up.
cf.
confer 		Compare
Conjecture A result that is thought to be true but no proof exists.
Corollary A smaller result that is a consequence from a larger theorem.
e.g.
exempli gratia 		For example
ergo Therefore
errata Errors, usually referring to a list of corrections made since the last edition.
et al.
et alia 		And others
etc.
et cetera 		And so on
Hypothesis A proposal consistent with known data and not shown to be true or false.
i.e.
id est 		That is
ibid.
ibidem 		The same place. Usually means the reference being used is the same as the previous one.
iff
if and only if 		The preceding and subsequent statements are equivalent.
L.H.S.
Left Hand Side 		Refers to the left side of the equality in an equation and similar for inequalities etc.
Lemma A statement and proof, relatively unimportant in their own right usually given in work towards a more substantial result such as a theorem.
modus ponendo tollens If both statements A and B can't be true, and we know that A is true, we know that B is false.
modus ponens If statement A implies B, and we know that A is true, then B is also true.
modus tollens If statement A implies statement B and we know that statement B is false, then A is false.
n.b.
nota bene 		Note well
Q.E.D.
quod erat demonstrandum 		That which was to be proved. Given at the end of a proof.
Q.E.F.
quod erat faciendum 		That which was to be shown. Given at the end of a calculation.
R.H.S.
Right Hand Side 		Refers to the right side of the equality in an equation and similar for inequalities etc.
reductio ad absurdum Reduction to absurdity. "This implies an absurtity and so is false." Proof by contradiction.
s.t.
such that 		such that
Theorem A statement that has been proven from already established facts.
w.l.o.g.
without loss of generality 		An argument is to be used for a specific case, which is easily applied to the others.
w.r.t.
with respect to 		Referring to

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