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.
bondâšt (#), arzâqâzé (#)
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. Axioms serve as the starting point of other mathematical statements called → theorems. 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
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.
Of, relating to, or resembling an → axiom.
Fr.: système axiomatique
Any system of → logic which explicitly states → axioms from which → theorems can be → deduced.
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.
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.
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.