The Wiki article you cite doesn’t mention the AP stylebook. Informality may or may not be the reason it isn’t used. Not that it matters. Its lack of use in this context means that it is not seen by readers. Why it isn’t used is less important to the question of whether people would recognize it than its replacement by the words about or approximately.
Interestingly, one of its approved uses hasn’t been mentioned yet. Apparently the Chicago Manual of Style requires a tilde as a line break indicator inside a long URL. Yet another usage that wouldn’t make “about” recognized as its meaning.
It can be used for equivalence relations. x ~ y would mean that x and y are in the same equivalence class. But there, it’s not a prefix/unary operator.
I don’t have access to the AP Stylebook to verify, but Google Gemini says there are explicit rules against using the tilde or plus sign as word replacements for ‘approximately’ and ‘and’.
There are exceptions to allow them for brand-names, LGBTQ+, and others.
I was half wrong. Tilde is not explicitly forbidden as approximately (in the 56th edition). There are rules in the Accent Marks section for usage in names and foreign language, but not a tilde in the Punctuation section. I think the absence makes it implicitly forbidden, but not positive.
One use I’ve not seen mentioned is asymptotically equal f(x) ~ g(x) means the limit of f(x)/g(x) =1. x would typically be approaching 0 or infinity known by context.
Does anyone know why the tilde was considered important enough to be included on keyboards in the first place? With limited space for characters, it’s not clear why the tilde was included when it is used so rarely. It could be that the ~ character was used in an early computing environment, which would explain why it’s found on computer keyboards. What about regular typewriters? Did the typewriters which predated computers have a ~ key?
Tildes weren’t on the old manual typewriters according to my recollection and a brief websearch. The really old ones didn’t even have a “1” key and the tilde is to the side of that. For 1 you would use a lower case L. For ! you would do an apostrophe and then backspace and do a period.
I just did a little research and some older typewriters had tildes and accent marks as “dead keys” since they were always used over letters. You would hit the key and it would print but the carriage didn’t move forward so you could then type the letter it would go over.
Just looked at the two broken IBM Selectrics that for some reason live in my basement, and neither has a ~. They do have ¼, ½, and ±. Also ¢ instead of ^. To me that means there was room to put a tilde if they thought it was important enough, but chose other symbols. Some keys can type more than two characters, so it is probably a limit of what fits on the ball rather than how many keys there are.
ETA: More than two characters per key is probably a reflection of what is on the ball, rather than what the key is able to produce. Some balls make [ and ], others make a 1 or ±., not a single key that can do all four symbols
Yeah, more than two characters per key would require another key analogous to Shift (like Control and Alt on computer keyboards), and if you had that, you’d probably put three (or four) characters on every key.