Is there a single verb meaning to make something equivalent to something? I want to use this possibly existent word to express the following:

"We transformed Problem A into the following problem B, which is proved equivalent to Problem A."

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    How would you use the word you're asking for? Could you provide a sample sentence with a blank in it? – Andrew Leach Jul 12 '14 at 18:23
  • I'm more familiar with 'Problem A and Problem B were known to exist; solving problem B was proved to be equivalent to solving problem A'. (Doesn't this arise with Fermat's Last?) – Edwin Ashworth Jul 12 '14 at 20:08
  • Just say "We proved problem A and problem B were equivalent." Do you need to use a word like "equivalentized"? – Peter Shor Aug 27 '15 at 11:56

Per the Cambridge Dictionary, to equate means:

to consider one thing to be the same as or equal to another thing.

while to equalize (UK: equalise):

to make things or people equal.

To correspond:

to be similar or the same in some way:

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  • Depending on context, normalize may also be used. – Wayfaring Stranger Jul 12 '14 at 22:33

To equalize:

  • To make uniform.
  • make equal, uniform, corresponding, or matching: let's equalize the duties among all employees in our office.


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Both equable and equatable are closely related to equal, though equable is derived not from equal but from the words’ shared root—the Latin aequus, meaning even or level.1 2 Equitable is distantly related to these words, but it comes directly from equity, which means (among other things) the state or quality of being just and fair.1

Your spell check might try to make you change equatable to equitable, but spell check is wrong on this one. Equatable is a perfectly good word. It can cause confusion, however, because it’s much rarer than equitable. Unless context makes equatable‘s meaning clear, consider synonyms such as similar, analogous, or comparable.


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Mathematicians use rearrange as a verb when they transform one equation into an equivalent equation.

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In topics such as NP-completeness, the word reduce is used in the following sense:

Reduce transitive verb 9b : to transpose from one form into another : convert - M-W

Interestingly, NP-complete problems are said to reduce to one another. More generally:

In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem. - Wikipedia

To say that Problem B reduces to Problem A carries the idea that Problem B can be proved to be equivalent to A.

Note that the negation of the reduce doesn't quite correspond to the negation of the idea. "Problem C does not reduce to Problem D" carries the idea that Problem C can be proved to be different from Problem D. If the equivalence is unknown (i.e. not provably equivalent and not provably different), one can say that Problem E has not been shown to reduce to Problem F.

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Equivalent and equal are not the same in mathematics. So "equalize" is not acceptable. Is there such a thing as "equivalize" ?

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