Parallelized and Equivalent

noun

• A person or thing equal to another in value or measure or force or effect or significance etc.
  • usage: "send two dollars or the equivalent in stamps"
• The atomic weight of an element that has the same combining capacity as a given weight of another element; the standard is 8 for oxygen.
  • synonyms: equivalent weight, combining weight, eq

adjective

• Being essentially equal to something.
  • usage: "it was as good as gold"; "a wish that was equivalent to a command"; "his statement was tantamount to an admission of guilt"
  • synonyms: tantamount

• (a.) Equal in measure but not admitting of superposition; -- applied to magnitudes; as, a square may be equivalent to a triangle.
• (n.) A combining unit, whether an atom, a radical or a molecule; as, in acid salt two or more equivalents of acid unite with one or more equivalents of base.
• (v.t.) To make the equivalent to; to equal; equivalence.
• (n.) That comparative quantity by weight of an element which possesses the same chemical value as other elements, as determined by actual experiment and reference to the same standard. Specifically: (a) The comparative proportions by which one element replaces another in any particular compound; thus, as zinc replaces hydrogen in hydrochloric acid, their equivalents are 32.5 and 1. (b) The combining proportion by weight of a substance or the number expressing this proportion, in any particular compound; as, the equivalents of hydrogen and oxygen in water are respectively 1 and 8, and in hydric dioxide 1 and 16.
• (n.) Something equivalent; that which is equal in value, worth, weight or force; as, to offer an equivalent for damage done.
• (a.) Contemporaneous in origin; as, the equivalent strata of different countries.
• (a.) Equal in wortir or value, force, power, effect, import, and the like; alike in significance and value; of the same import or meaning.

Equivalent is a concept in probability theory that means that two probability measures (q. V.) assign a probability of zero to precisely the same sets. Example: If the probability space corresponding to two flips of a fair coin is W = {HH, HT, TH, TT}, and two probability measures, P(.) and Q(.), both assign a probability of zero to the empty set, P(Æ) = Q(Æ) = 0, and to no other set, then they are equivalent probability measures.