Correct Usage of Equal and Equivalent in Math Statements
Date: 02/20/2008 at 11:43:16 From: Valerie Subject: when do I use equal and when do I use equivalent properly? Is there a mathematical difference between equal and equivalent and if so, what is the difference? For example: Are two algebraic expressions (with the same solution set) equivalent or equal? Are two numeric expressions (with the same value) equal or equivalent? For example: is 10^4 equal to OR equivalent to 10 x 10 x 10 x 10? We would write an equal sign between the two numeric expressions given above, but would we "say" they were equivalent or equal? Would we write a question properly that reads: Find an expression that is equal to OR equivalent to 10^4. ?
Date: 02/20/2008 at 23:45:39 From: Doctor Peterson Subject: Re: when do I use equal and when do I use equivalent properly? Hi, Valerie. Sometimes I think the terms "equal" and "equivalent" are, well, equivalent; their meanings overlap, and the precise distinction can vary from one case to another. But in general, equal means that two entities are the same entity equivalent means that two entities have the same EFFECT, in some sense Two expressions can be called equal for some specific value of the variable, because they yield the same number; they are equivalent when they are ALWAYS equal--true for any value of the variable. So here "equivalent" is a stronger term. Two equations are equivalent when they have the same solution set. (Note: an expression doesn't have a solution set!) You would never say that two equations are equal, because that would get very confusing! Two sets are equivalent when they have the same cardinality (number of elements); they are equal when they are actually the same set (consisting of the same elements). Here "equal" would seem to be the stronger term! Two fractions are equivalent when their values are equal; here I think the only reason to use the word "equivalent" rather than "equal" is to emphasize that they are two DIFFERENT ways to express the SAME value. In your question about numerical expressions, I think "equivalent" would be the better choice, because, as with fractions, the emphasis is on an expression that looks different but has the same numerical value after you evaluate it. It wouldn't be wrong to say "equal", but this just feels a little more right. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.