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Equal vs Equivalent: Finer differences in meaning and usage?

What would be the subtler differences & similarities?

Examples & scenarios where:

  • Only one can be used
  • Both can be used
  • One is more apt
  • Changing one with the other changes the meaning / specificity of meaning
  • Equal means having some dimension in common (price, volume, meaning, etc -- This X is equal to that one -- whereas equivalent means 'is a satisfactory substitute for'. And substitution requires a context. Mostly any kind of "subtle differences" depend on the context, not the words. Or else they're just individual habits that are felt to be universal because they don't contradict anything. – John Lawler Apr 5 '16 at 16:36
  • Aluminum wire conductors will be larger, but lighter, than equivalent copper wire conductors, based on equal conductance. Use equivalent when referring to things you can easily tell apart, but which are interchangeable. 1/2 cup olive oil is equivalent to 2/3 cup butter. – Phil Sweet Jun 22 '16 at 3:57
  • Then all people are "Equal" in the eyes of god/ legal system.. ? or are they actually Equivalent, despite different gender, faith, sexual orientation etc.? – Alex S Jun 22 '16 at 4:44
  • @MaxWilliams - My cousins kids have homework. I have not had homework in 10+ years. Stop being whatever you are being. I've spent years with my grandfather who used to say Man & woman are not equal but equivalent. Hence, I am wondering how this works in the above 4 scenarios. Just language curious/ pondering. No homework PS: Homework. ha ha! you're ridiculous. From start Apr to June end some student has this for homework - You've got some paranoid imagination – Alex S Jun 22 '16 at 12:59
  • @AlexS Regardless of my mental state, there are a lot of questions posted here which have been directly copied from people's homework. They stand out because they contain no comment from the poster: no explanation, no context, no previous research etc: they consist of a question and often a "Multiple choice" style list of answers. Your question has this exact format, so if I have made a mistake in thinking it was one of those questions, then that's a natural mistake to make. A man who sees another man in a gorilla suit and thinks it's a gorilla is not paranoid, he has simply been fooled. – Max Williams Jun 22 '16 at 13:10
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They have different meanings in mathematics.  As Mike says, equality (represented by “=”) means that two things are the same.  For example, 3 = 3 = 3.0 = 1+2 … and an infinite variety of other ways of expressing the same number, but 3 does not equal any other number.

Equivalence is much more loosely defined.  An equivalence relationship (typically represented by “≅”) is any relationship that satisfies the following properties:

  • Reflexive: For any object X, it is true that X ≅ X.
  • Symmetric: For any X and Y, if X ≅ Y, then Y ≅ X.
  • Transitive: For any X, Y, and Z, if X ≅ Y and Y ≅ Z, then X ≅ Z.

Clearly equality satisfies the above properties, so equality is an equivalence relationship.  (In other words, equality is a subset (a special case) of equivalence.)  But equivalence relationships can be more interesting.  One of the best known equivalence relationships is modulo.  For example, in the modulo 10 equivalence relationship, 3 ≅ 13 ≅ 23 ≅ 33 …

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  • I like the answer, and I am hoping for more thoughts on usage beyond math; in real life. – Alex S Jun 22 '16 at 13:04
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"Equal" and "equivalent" are equivalent, but they're not equal. :-)

They have similar, but not identical meanings. Equal means the same thing, but equivalent means that one can frequently be substituted for the other.

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  • But then you get phrases such as "equal but different", implying that two things are of the same value or rank, but are not the same thing. – Simon B Apr 6 '16 at 7:29

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