# General mathematical vocabulary

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 Phrase Definition ﻿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. ﻿iffif 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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