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For instance, for addition this is called the sum: $\underbrace{x+y}_{\text{summands}} = \underbrace{z}_{\text{sum}}$

But what is this called for a unspecified operation? $\underbrace{x\circ y}_{\text{operands}} = \underbrace{z}_{\text{what is the name of this?}}$

Thomas Andrews
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Frank Vel
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  • I would just call it result (of $\circ$)? – Henrik supports the community Jan 15 '15 at 15:25
  • Yeah, even operand is likely to be ambiguous, unless the operation is commutative. (And operand is often used for unary and ternary operators, too.) I've always thought of "summand" and its ilk as ancient terms used before mathematics developed good notation. :) – Thomas Andrews Jan 15 '15 at 15:34
  • @ThomasAndrews Which is funny because multiplication has two names, multiplicand and multiplier. But I think it's nice to have a name for things in general, instead of just some symbol. – Frank Vel Jan 15 '15 at 15:38
  • Sorry, but you are arguing based on symmetry. Language doesn't work that way. We can make up words for stuff, but it isn't always useful or clarifying. – Thomas Andrews Jan 15 '15 at 15:39
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    Multiplication has separate names for the two operands because there are quite a few multiplications which are not commutative, so it matters which. Just as subtraction has different terms for the operands, (minuend, subtrahend.) Honestly, knowing these names is the stuff of grade school forced memorization that adds zero understanding to the operations. – Thomas Andrews Jan 15 '15 at 15:42
  • @ThomasAndrews They shouldn't necessarily be taught at grade school, but they could still exist, especially for general cases. Also, if it's not commutative then it shouldn't be called multiplication. That's just evil... – Frank Vel Jan 15 '15 at 16:01
  • @fvel Matrix multiplication is noncommutative (along with many more exotic examples) – Christopher Jan 15 '15 at 16:01
  • The terms exist, sure, but nobody ever uses minuend except to torment school children into memorizing them. There are a lot of terms we don't learn, because they add no knowledge. And quite a lot of multiplication is non-commutative. Get ready for it. – Thomas Andrews Jan 15 '15 at 16:11
  • In any event, you can get very far in mathematics without ever knowing the words summand, minuend, etc. Far more valuable is knowing the existence of non-commutative multiplications. :) – Thomas Andrews Jan 15 '15 at 17:00
  • @ThomasAndrews I tend to think of multiplication as something defined on numbers, while matrix multiplication is just just using the word multiplication as an analog, because multiplication of numbers is involved. And while you can get far without knowing those words, it's still nice to have them in the few circumstances they're applicable. Because what is mathematics but a generalisations of concepts? As long as we have a concept of a summand, I think it should have a name. – Frank Vel Jan 15 '15 at 17:21
  • Except that there are quite a few useful "rings" with non-commutative multiplications, like quaternions. I don't see how it is "nice" to know these words. They are just random assignments of terms we never need to use. It adds no value, except perhaps when playing Scrabble or solving word puzzles. – Thomas Andrews Jan 15 '15 at 17:25
  • @ThomasAndrews I forgot about those! Although since multiplication is a binary operation you could get away by saying "left/right multiplicand". It's nice to have a name for a thing when you're explaining it as well instead of pointing to it and saying "This thing on the right hand side of the equation". What if we didn't have a word for 3 but just said "one-one-one"? But sure, too many would just be cluttering and probably make reading math harder... – Frank Vel Jan 15 '15 at 17:39

3 Answers3

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Speaking of the "value" or "result" of the operation would by far be the most understandable.

hmakholm left over Monica
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You show "sum" as the result of the function "sum."
If you do not insist on the sought-after word beginning with "oper-," how about -- "result?"

Senex Ægypti Parvi
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Generalizing the question to functions, note that $\circ$ is just a binary function $\circ(x,y)=z$ but expressed with infixed notation $x\circ y$, in my opinion the common terminology is: given a $n$*-ary function* $f:X_0\times X_1\times...\times X_n\rightarrow Y$

$$f(x_0,x_1,...x_n)=y$$

arguments : $x_0,x_1,...x_n$ are the elements af the domains $X_0, X_1,...X_n$

value : $y$ is the image of the $n$*-uple* $(x_0,x_1,...x_n)$ via the function $f$ and belongs to the codomain $Y$

Note: from wikipedia we get this definition

A value of a function is the result associated to a value of its argument (also called variable of the function)

MphLee
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