> Typically we write that the solution is "x = –2"
That is not overloading "=" at all. It is overloading the word "solution".
What your teacher probably told you is:
"x+3=1 is equivalent to x=-2 by .... Hence, the solution of x+3=1 is the same the solution of x=-2 (which is -2 in both cases). Since the solution of x=-2 is so obvious, we also say the solution is x=-2 to mean that it is the same solution as of the equation x=-2."
Same difference as in "Q:Would you like a large coffee or a small coffee? A: Large "
The correct answers should only be either phrase "A large coffee" or "a small coffee", but the answer was an adjective.
I don’t know the precise definition of overloaded. I was merely claiming that the use of = in an equation, like a polynomial equation, is very much different than the use of = in something like the statement of the distributive property of the real numbers.
I’m a mathematician so it’s something my teacher said as such but something that I noticed consciously when I started doing some programming.
That is not overloading "=" at all. It is overloading the word "solution".
What your teacher probably told you is:
"x+3=1 is equivalent to x=-2 by .... Hence, the solution of x+3=1 is the same the solution of x=-2 (which is -2 in both cases). Since the solution of x=-2 is so obvious, we also say the solution is x=-2 to mean that it is the same solution as of the equation x=-2."
Same difference as in "Q:Would you like a large coffee or a small coffee? A: Large " The correct answers should only be either phrase "A large coffee" or "a small coffee", but the answer was an adjective.