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Which I did with a concrete example, which you have since ignored.

You have given nothing of that sort. You provided a statement about a completely orthogonal topic instead. "Prove that the sky is blue" -- "Here, grass is green" -- "That doesn't answer the question" -- "Nu-uh it does!". That's you. That "Nu-uh".

The inverse of frac is to invert the fraction - happy now?

"Inverting a fraction" is not a functional inverse. You're getting led astray by terminology, those two uses of the word "invert" have nothing to do with each other, it's a case of English having bad terminology (in German we use different terms so the confusion doesn't even begin to apply).

Go read that wikipedia article I linked. Can you even read it. Do you have the necessary mathematical literacy.

No, they’re not. Division is a binary operator, a fraction is a single term.

Do you want to tell me that fractions don't take two numbers? That two numbers applied to division don't form a term?

Multiplication is also a binary operator, a and division is the opposite of it

Inverse. I read elsewhere that you're a math teacher and this is just such a perfect example of what's wrong with math ed: Teachers don't even know the fucking terminology. You don't know maths. You know a couple of procedural rules you shove into kids, rules that have to be un-taught in university because nothing of it has anything to do with actual maths.

No, it’s a mnemonic to remind people of the actual rules.

There's no such thing anywhere but in the US. Those rules are a figment of the imagination of the US education system.

You are up to your scalp in the Dunning-Kruger effect. Two possibilities: You quadruple down and become increasingly bitter, or you find yourself an authority that you trust, e.g. a university professor, and ask them in person. Ask a Fields Medalist if you can get hold of one. You think you know more about this than me. Motherfucker you do not, but I also acknowledge that I'm just some random guy on the internet to you.

If you want to continue this, I have one condition: Explain, in your own words, the difference between syntax and semantics. If you have done that, done that homework, I'm willing to resume your education. Otherwise, take the given advice and get lost I've got better things to do than to argue with puerile windbags.