You truly know nothing about math. Do yourself a favor and look up a term before spouting off nonsense about it.

Mapping is a commonly used math term. A reflection is a type of mapping.

From Britannica (online) - although you can find similar definitions in many places :

Mapping : any prescribed way of assigning to each object in one set a particular object in another (or the same) set. Mapping applies to any set: a collection of objects, such as all whole numbers, all the points on a line, or all those inside a circle. For example, “multiply by two” defines a mapping of the set of all whole numbers onto the set of even numbers. A rotation is a map of a plane or of all of space into itself. In mathematics, the words mapping, map, and transformation tend to be used interchangeably.

You revel in your willful ignorance of math. You puff out your chest and promote yourself as the folk-wisdom hero who must bring down all mathematical evil-doers. How's that going for you? Have you ever taken my advice and sent your math musings off to prestigious journals for publication?

There is nothing about the definitions of "addition", or "subtraction" which requires that the result be other than the starting number. — Metaphysician Undercover

That's correct. There is also nothing about the definition of "negation" which requires that the result be other than the starting number.

"Negation" is defined as producing a statement other than the one which is negated. — Metaphysician Undercover

You're equivocating. The subject is numbers, not statements.

You provided a definition of "additive inverse", not of "opposite", nor of "negation". — Metaphysician Undercover

Negation, as a mathematical operation, is the additive inverse.

And, as I've told you already, your quote only demonstrates that mathematics uses these terms in a way which is inconsistent with other fields of study, like philosophy and logic. — Metaphysician Undercover

No, it does not. Different fields have their own specialized terms. Recognize the context and equivocation can be avoided.

In fact, I see now that there is inconsistency within the quoted paragraph itself. It says: "For a real number, it reverses its sign". And it also says: "Zero is the additive inverse of itself." Since zero is a real number then it is an exception to the stated rule for real numbers, therefore the inconsistency inheres within your definition. It is self-contradicting, stating a rule then a contradicting rule. — Metaphysician Undercover

That is not part of the definition, that is commentary. To negate a number is to subtract it from zero. It's very simple.

That follows from the group-theoretic definition which @Real Gone Cat kindly provided earlier. The real numbers (and, separately, the integers) are a group under addition, where 0 is the identity element and 0 is its own inverse.

Which is to say, the negation of zero is zero. If you disagree, then you shouldn't trust a calculator since it treats -0 as a valid operation.

Notice, negation takes the proposition to "another proposition". There is no exception, which would allow that a negated proposition could remain the same, as you propose with zero. — Metaphysician Undercover

As noted above, a number is not a proposition.

To negate a number is to subtract it from zer — Andrew M

Again, we were not talking about mapping. Your analogy was stated explicitly as "To be across from something means to be reflected in a line, point, or plane."

"To be across from something" as in opposite to it, does not imply mapping. If you would have been up front in the first place, and said that you were describing opposite as mapping, instead of as a reflection, I would have rejected that right off the bat. Instead, you tried to use the ambiguity of "opposite" to lead you to "across from", then on to "reflection", and finally "mapping". That's nonsense to describe "opposite" as "mapping".

How's that going for you? — Real Gone Cat

It's going very well, thank you for asking. I find it quite amusing, a lot of fun, and a good source of entertainment. I sincerely hope it is as much fun for you as it is for me. Then we're both winners here.

You're equivocating. The subject is numbers, not statements. — Andrew M

The subject is "inverse", and "opposite", and whether mathematics uses a perverse meaning for the words, which allows that a term such as "zero" might be opposite to itself.

In our inquiry as to whether this is the case or not, we can either adhere to the logical definition of "negation", or move to some perverted definition of "negation" which you propose, ("To negate a number is to subtract it from zero"), devised by you to be consistent with a perverted meaning of "opposite", and "inverse".

Of course, we ought to adhere to the logical definition of "negation" and not succumb to the perverted definition, because then we would not grasp the perversion which is present, and not see that mathematics has perverted the meaning of "opposite" and "inverse", to allow zero to be opposite to itself.