associative axiom bondâšt-e âhazeš Fr.: axiome d'associativité A basic rule in → group theory stating that if a, b and c are members of a group then (a * b) * c and a * (b * c) are members of the group. → associative; → axiom. |
axiom bondâšt (#), arzâqâzé (#) Fr.: axiome In any system of mathematics or logic, a statement or proposition from which secondary statements or propositions are derived. The truth of an axiom is either taken for granted or assumed. In modern practice, axiom and → postulate have the same meaning. M.Fr. axiome, from L. axioma, from Gk. axioma "authority," literally "something worthy," from axioun "to think worthy," from axios "worthy," from PIE adj. *ag-ty-o- "weighty," from base *ag- "to drive, draw, move." Bondâšt, literally "taking as the base," from bon
"root, origin, base" + dâšt "held," from dâštan "to have,
to hold, to maintain, to consider." |
axiom of constraints bondâšt-e pâvandhâ Fr.: axiome des contraintes An axiom in → statics, stating that any → constrained body can be treated as a → free body detached from its → constraints, provided the latter are represented by their → reactions. → axiom; → constraint. |
axiomatic bondâšti Fr.: axiomatique Of, relating to, or resembling an → axiom. |
axiomatic system râžmân-e bondâšti Fr.: système axiomatique Any system of → logic which explicitly states → axioms from which → theorems can be → deduced. |
closure axiom bondâšt-e bandeš Fr.: axiome de clôture A basic rule in → group theory stating that if a and b are a group element then a * b is also a group element. |
identity axiom bondâšt-e idâni Fr.: axiome d'identité A basic rule in → group theory stating that there exists a unit group element e, called the identity, such that for any element a of the group a * e = e * a = a. |
inverse axiom bondâšt-e vârun Fr.: axiome d'inverse A basic rule in → group theory stating that for any element a of a group there is an element a^{-1} such that a * a^{-1} = a^{-1} * a = e. |