equivalent

Pluralequivalents

1. 1
   adjective

   Similar or nearly identical to something else in value, meaning, or effect: virtually equal.

   Her new job offers a salary equivalent to what she earned abroad.

   The committee ruled the two qualifications equivalent for admission purposes.

   Similarequal, comparable, corresponding, similar, interchangeable

   Oppositedifferent, unequal, dissimilar

   Note

   The everyday sense, and the one the technical senses sharpen: Latin aequivalēns meant "having equal power," built from equi- and -valent. It normally takes to (a thirty-minute jog is equivalent to a couple of hamburgers). Older prose could also set it after its noun, as Robert South does when he calls servile and ministerial "terms equivalent."

2. 2
   nouncountable

   Something that is virtually equal to another thing, or has the same value, force, or effect.

   Engineers searched for a cheaper equivalent that would withstand the same heat.

   In ancient trade, a measure of salt served as the equivalent of currency.

   Similarcounterpart, substitute, alternative, equal, match

   Note

   As a noun it usually takes of, and the phrase can carry real rhetorical weight: in 1977 Jimmy Carter called the national energy effort the "moral equivalent of war." Older prose also used it on its own for something offered in exchange. Macaulay's History of England (1849) says Protestants were "entitled to an equivalent" if the Test Act were repealed.

3. 3
   adjective

   Of two sets, having a one-to-one correspondence between their members.

   The set of vowels and the set {1,2,3,4,5} are equivalent, since each letter pairs with one number.

   Two sets are equivalent precisely when their members can be paired off one to one.

   Similarequinumerous

   Note

   Set theory uses the word to say two collections are the same size without counting them. Equivalent sets need not share a single member. They need only pair off completely, which is why they are said to have the same cardinality and why equinumerous serves as a synonym. The idea reaches past counting: E. Kamke's Theory of Sets (1950) observes that all enumerable sets are equivalent to each other, but not to any finite set.

4. 4
   adjective

   Having an equal capacity to combine chemically with other substances.

   Chemists treated the two reagents as equivalent because each combined with the same quantity of acid.

   Hydrogen and a single charge of chlorine are equivalent in combining power.

   Note

   Chemistry applies the adjective to quantities that combine in matching proportions: equivalent amounts react with, or replace, the same amount of another substance. The measure behind it is the noun for equivalent weight, and the two travel together. Quantities count as equivalent because each amounts to one equivalent.

5. 5
   nouncountable

   The mass of a substance that combines with or replaces a standard amount of another, known as its equivalent weight.

   To balance the reaction, add one equivalent of base for each equivalent of acid.

   The chemist calculated the equivalent of the unknown salt from the titration data.

   Note

   Chemists clip equivalent weight to a single word, and the noun turns combining power into a number. It names the mass that reacts with or displaces a fixed amount of hydrogen or oxygen, which works out as molar mass divided by valence. It is the quantity that makes the combining-power adjective measurable.

6. 6
   adjective

   Of magnitudes, equal in measure but not able to be laid exactly over one another.

   A parallelogram and a triangle on the same base may be equivalent though differently shaped.

   The two figures are equivalent in area but cannot be superimposed.

   Note

   Geometry keeps this word for figures that match in size but not in shape. A square may be equivalent to a triangle: the two have the same area, but there is no way to lay one over the other so that they coincide. Figures that do coincide are congruent, and that is the distinction to hold onto. Equivalent compares measure alone, while congruent compares everything.

7. 7
   adjective

   Of a map projection, preserving area so that regions appear in their correct relative sizes.

   The atlas used an equivalent projection to compare the true sizes of continents.

   On an equivalent map, Greenland no longer dwarfs Africa.

   Similarequal-area

   Note

   Cartographers use it as a synonym for equal-area. An equivalent projection keeps every region at its true relative size, and it pays for that in shape. Outlines and angles are necessarily distorted somewhere on the map. Choosing an equivalent projection means deciding that comparing sizes matters more than drawing coastlines faithfully.

8. 8
   adjective

   Of elements, related by an equivalence relation, so that they count as belonging to the same class.

   Integers that differ by a multiple of twelve are equivalent under arithmetic modulo twelve.

   Two elements are equivalent when the relation places them in the same class.

   Similarcongruent

   Note

   Here sameness comes from a chosen relation rather than from size. Any relation that is reflexive, symmetric and transitive sorts elements into classes, and members of one class are equivalent. Unlike the set-size meaning, which compares whole sets, this compares individual elements. Mathematicians usually name the relation, as in equivalent under rotation or equivalent modulo twelve, because the word alone does not say which sameness is meant.

9. 9
   adjective

   Of two categories, related by a pair of functors so that one is essentially a relabeling of the other.

   The category of Boolean algebras and a category of certain spaces turn out to be equivalent.

   Two categories are equivalent when functors connect them with no loss of structure.

   Note

   Category theory uses the word for a deliberately loose kind of sameness. Two functors run back and forth between the categories, and a round trip need not return each object exactly. It only has to be naturally isomorphic to the identity functor. That slack is the point. It is weaker than isomorphism of categories, which demands an exact return, and it makes precise the informal idea that one category is the other relabeled.

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