What's the difference between operators and functions?

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Discussion Overview

The discussion centers around the distinction between operators and functions, exploring their definitions and applications in mathematical contexts. Participants examine whether operators can be considered a specific type of function and how different notations (infix vs. functional) influence understanding.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that any binary operation can be viewed as a function from S × S to S, highlighting the convenience of infix notation.
  • Others clarify that the term "operator" typically refers to a function defined on functions, contrasting it with functions that operate on numbers.
  • A participant questions whether the term "SUM(x,y)" should be classified as an operator or an operation, suggesting it may not fit the definition of an operator.
  • There is acknowledgment of ambiguity in the original post regarding the terminology used.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and distinctions between operators and functions, indicating that the discussion remains unresolved with multiple competing interpretations.

Contextual Notes

The discussion reveals limitations in the clarity of terminology, with participants noting that mathematical texts may use the terms "operators" and "functions" in distinct ways, leading to potential confusion.

SW VandeCarr
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Is there a fundamental difference between operators and functions?

For example we could have F(x,y)=x+y or we could write SUM(x,y) where SUM is a defined operation in some program. Could operators be considered a particular type of function?
 
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Yes. Any binary operation on [itex]S[/itex] is simpy a function from [itex]S \times S \to S[/itex]. We use infix notation (that is, we write the function in between the operands as in x + y instead of +(x, y) ) out of convenience and familiarity.
 
Moo Of Doom said:
Yes. Any binary operation on [itex]S[/itex] is simpy a function from [itex]S \times S \to S[/itex]. We use infix notation (that is, we write the function in between the operands as in x + y instead of +(x, y) ) out of convenience and familiarity.

Thanks Moo Of Doom. I was pretty sure of this, but math texts usually use these in terms in distinct ways.
 
Last edited:
Moo of Doom talked about "operations". Your question was about "operators". Generally, an "operator" is a function defined on functions as opposed to functions on numbers.
 
HallsofIvy said:
Moo of Doom talked about "operations". Your question was about "operators". Generally, an "operator" is a function defined on functions as opposed to functions on numbers.

Then SUM(x,y) would not be read as an operator on (x,y), but rather as an operation on (x,y)?
 
Yes, that is true. The original post was ambiguous.
 

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