It's used in german mathematics education (secondary level), either to mark a contradiction in a proof or more generally to mark an erroneous statement.

But I have never seen it to mark negation of a condition, that's usually done with a slash (as in ≠ ≮ ≯ ≰ ≱ ≴ ≵ ⊄ ⊅ ⊈ ⊉ ⊊ ⊋ ∉ ∌ ∄ ∦, you get the idea).

So for "not a right angle" I'd have expected a "right angle" symbol with a slash through it.

Funny enough, I've only seen it at the Gymnasium (secondary level) and not in the University a few years later -- then indeed the usual symbols were the 'slashed' relations like you've described, or the bottom symbol: ⊥ in logic. Maybe it's an idiosyncrasy of a certain subset of math teachers.

But how would you position the slash to get a somewhat easy to decipher symbol? To me, the right angle symbol seems to lend itself more to this unorthodox negation through the contradiction symbol than to negation through the normal slash.

Also in Dutch universities to mark a contradiction, especially in a proof by contradiction.

Same. Never seen that symbol in my life. I've seen ¬, ~, !, etc used for not/negation in computer science, math, logic, etc.

And some commenters said they used it to mark proof by contradiction, but why is there a need to mark it when you are showing it via proof? A canonical example of proof by contradiction is proving sqrt(2) is not rational. Never have I seen it marked with that symbol. Where would you even mark it? At the beginning with the assumption? Or at the end like QED?

Math degree holder from Iowa, yeah, I've seen and used it many times. The symbol is used when you reach the contradictory statement. Like "1 = 2".

"By way of contradiction suppose P, then ..., thus ~P ↯. Therefore ..."

I've actually always wanted a way to mark "the contradiction" once I've obtained it. Thanks!

To me that reads: I throw your assumption into the GROUND!

I was taught it in extracurricular mathematics in Australia. We were taught that it goes at the end of a contradiction proof once the contradiction has been found. We used to write it extra large, like lightning strike. I think of it like a proof mic-drop.

It's the first symbol referenced for symbols used in proof by contradiction to show contradiction [0]. I know that's not exactly "not" or "disproof" but I think that might be what the poster was getting at.

[0] https://en.wikipedia.org/wiki/Contradiction#Symbolic_represe...

I believe I have seen it used as a symbol which indicates the discharge of an assumption, but never for "not".