Word |
Explanation |
ansatz |
'an educated guess' |
axiom |
a mathematical statement which is accepted as true without a proof in order to start somewhere and derive a theory |
characterization theorem |
a result which says that two mathematical statements are equivalent |
closed-form expression |
often used in the context of real or complex calculus to describe a mathematical expression which consists only of real or complex arithmetic and such that any functions present in the expression are only the elementary functions |
conjecture |
a result which has not yet been proven but which is strongly suspected to be true |
corollary |
a result which follows effortlessly from another result |
exercise |
a light challenge which requires only the application of routine operations already known to the student (compare to 'problem') |
factorization |
a multiplicative-type algebraic operation (e.g. integer multiplication, binary set intersection, ...) repeatedly applied (compare to 'partition') |
gedankenexperiment |
'a thought experiment' |
hypothesis |
a word deriving from latin, being a synonym for 'assumption' |
lemma |
a supporting result, something used to reach a theorem or a proposition |
parameter |
in the context of a collection of mathematical object, a parameter refers to an element of the index set |
partition |
an additive-type algebraic operation (e.g. integer addition, binary set union, ...) repeatedly applied (compare to 'factorization') |
penultimate step |
the expression or statement from which the final theorem (or proof) follows with a single step of deduction |
portmanteau theorem |
|
postulate |
an archaic near-synonym for 'axiom' |
proposition |
a result of secondary interest |
problem |
a substantial challenge which requires perhaps even the invention of new methods not yet known to the student (compare to 'exercise') |
representation theorem |
|
subdefinition |
a synonym for a special case or a particular case of a definition |
subresult |
a synomym for special case or particular case of a result |
theorem |
a result of primary interest |
well-defined |
often used in the context to a function or a mapping recently introduced or defined, meaning that the mapping satisfies the actual definition of a map, being a right-unique and left-total binary relation |