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What defines an operator input/output for simple expressions

  1. Jan 5, 2013 #1
    Hello. I have some questions on operations.

    Suppose in the course of a derivation there is a mathematical statement of the form
    A+1=B+C
    then "+" is an operator acting on inputs "B" and "C".
    Question 1: Is the output of the operation "A" or the expression "B+C"?
    The reason I think the output may be "B+C" is because in the statement X=(Y+Z)+W, wouldn't the output of the first addition be Y+Z?

    Question 2: Since the equals sign "=" has two inputs, the left hand side (LHS) and right hand side (RHS) expressions, is it also an operator?
    How does one distinguish whether A+1 is the input or B+C is the input?
    If "=" is an operator, what is the output? If "=" is not an operator, what is it?
     
  2. jcsd
  3. Jan 5, 2013 #2

    I like Serena

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    Homework Helper

    Welcome to PF, benno! :smile:


    The operation "+" on B and C has as output indeed "B+C".

    The symbol "=" represents a "relation".


    Suppose we're only talking about the real numbers ##\mathbb R## with the regular addition "+" and the regular equality "=".


    Then, mathematically, "+" is a function, defined as:
    $$+: \mathbb R \times \mathbb R \to \mathbb R \qquad \text{ with }(x,y) \mapsto x+y$$
    That is, the plus function has two real numbers as input, and one real number as output.



    The relation "=" defined on the real numbers is the set:
    $$\{ (x,x) : x \in \mathbb R \}$$
    That is, two real numbers have an equality relation with each other if they are the same number.
    In your case "A+1" has an equality relation with "B+C".


    Btw, "=" can also be considered an operation.
    In that case both "A+1" and "B+C" are inputs, and the output is either "true" or "false".
     
  4. Jan 5, 2013 #3
    Thanks very much for the clear explanation. That was exactly what I was looking for.
     
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