equivalent

adj

1. Similar or identical in value, meaning or effect; virtually equal.

   “To burn calories, a thirty-minute jog is equivalent to a couple of hamburgers.”

   “For now to serve and to minister, servile and ministerial, are terms equivalent.”

   “A doorknob of whatever roundish shape is effectively a continuum of levers, with the axis of the latching mechanism—known as the spindle—being the fulcrum about which the turning takes place. Applying a force tangential to the knob is essentially equivalent to applying one perpendicular to a radial line defining the lever.”

   “Total activity levels in the lowest quartile were equivalent to walking for 49 minutes at roughly 3 miles (4.8 kilometers) per hour daily. Total activity levels in the second-, third- and fourth-highest quartiles were equivalent to 78, 105 and 160 minutes, respectively.”

2. Of two sets, having a one-to-one correspondence.

   “All enumerable sets are equivalent to each other, but not to any finite set.”

   “Equivalent sets should, by rights, have the same "number" of elements. For this reason we sometimes say that equivalent sets have the same cardinality.”

   “Finite sets A and B are equivalent sets only when n(A) = n(B) i.e., the number of elements in A and B are equal.”

   “The equivalence theorem: If both M is equivalent to a subset N₁ of N and N is equivalent to a subset M₁ of M, then the sets M and N are equivalent to each other.”

3. Relating to the corresponding elements of an equivalence relation.
4. Of two categories, (informally) such that one is essentially a relabeling of the other; (formally) related by a pair of functors such the composition of the one with the other is naturally isomorphic to the identity functor.
5. Having the equal ability to combine.
6. Of a map, equal-area.
7. Equal in measure but not admitting of superposition; applied to magnitudes.

   “A square may be equivalent to a triangle.”

noun

1. Anything that is virtually equal to something else, or has the same value, force, etc.

   “He owned that, if the Test Act were repealed, the Protestants were entitled to an equivalent, and went so far as to suggest several equivalents.”

   “Our decision about energy will test the character of the American people and the ability of the President and the Congress to govern. This difficult effort will be the "moral equivalent of war" — except that we will be uniting our efforts to build and not destroy.”

2. An equivalent weight.

verb

1. (transitive)To make equivalent to; to equal.