I love how the text seems to be right from the time where the symbol was already abstract, but it was still used as an et ligature instead of a standalone symbol

I think this is called aposiopesis

Noo! There will never be another like him :(

I’m not using logic in this case, you are just being insincere. Let me know when you bother to try to understand anything I or the authors of your holy textbooks wrote.

Apparently you can’t read either textbooks or wikipedia and understand it.

Also, wait, you’re just a tutor and not actually a teacher? Being wrong about some incredibly basic thing in your field is one thing, but lying about that is just disrespectful, especially since you drop that in basically every sentence.

We’ve been at this point, I’m not going to explain this again. But you weren’t able to read a single sentence of a wikipedia article without me handfeeding it to you, so I guess I shouldn’t be surprised. I’m sorry for your students.

Yeah, doesn’t mean that you know what an author is talking about when you encounter it doing actual math

The notation is not intrinsically clear, as any human writing. Ambiguous, one may say.

If you don’t want to see why you’re wrong that’s your thing, but I tried. I can just say, try to re-read the math textbook you took pictures of, and try to understand it.

Exactly! It’s in math textbooks, in both ways! Ambiguous notation, one might say.

You can define your notation that way if youlike to, doesn’t change the fact that commonly f^{-1}(x) is and has been used that way forever.

If I read this somewhere, without knowing the conventions the author uses, it’s ambiguous

Let me quote from the article:

“In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality x*(y+z) = x*y + x*z is always true in elementary algebra.”

This is the first sentence of the article, which clearly states that the distributive property is a generalization of the distributive law, which is then stated.

Make sure you can comprehend that before reading on.

To make your misunderstanding clear: You seem to be under the impression that the distributive law and distributive property are completely different statements, where the only difference in reality is that the distributive property is a property that some fields (or other structures with a pair of operations) may have, and the distributive law is the statement that common algebraic structures like the integers and the reals adhere to the distributive property.

I don’t know which school you went to or teach at, but this certainly is not 7th year material.

About the ambiguity: If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous. It’s correct notation in both cases, used since forever, but you need to explicitly disambiguate if you want to use it.

I hope this helps you more than the stackexchange post?

If you read the wikipedia article, you would find it also stating the distributive law, literally in the first sentence, which is just that the distributive property holds for elemental algebra. This is something you learn in elementary school, I don’t think you’d need any qualification besides that, but be assured that I am sufficiently qualified :)

By the way, Wikipedia is not intrinsically less accurate than maths textbooks. Wikipedia has mistakes, sure, but I’ve found enough mistakes (and had them corrected for further editions) in textbooks. Your textbooks are correct, but you are misunderstanding them. As previously mentioned, the distributive law is about an algebraic substitution, not a notational convention. Whether you write it as a(b+c) = ab + ac or as a*(b+c) = a*b + a*c is insubstantial.

Please learn some math before making more blatantly incorrect statements. Quoting yourself as a source is… an interesting thing to do.

https://en.m.wikipedia.org/wiki/Distributive_property

I did read the answers, try doing that yourself.

I don’t know what you’re on about with your distributive law thing. That just states that a*(b + c) = a*b + a*c, and has literally no relation to notation.

And “math is never ambiguous” is a very bold claim, and certainly doesn’t hold for mathematical notation. For some simple exanples, see here: https://math.stackexchange.com/questions/1024280/most-ambiguous-and-inconsistent-phrases-and-notations-in-maths#1024302

What does type() mean here?

The effective vibe is much more important than any underlying biology.

Tomatoes are vegetables.

If it’s networking related, I like “Layer 8 Issue”

Pemdas puts division and multiplication on the same level, so 34/22 is 12 not 3. Implicit multiplication is also multiplication. It’s a question of convention, but by default, it’s 16.

https://en.m.wikipedia.org/wiki/Order_of_operations

Well landau notation only describes the behaviour as an input value tends to infinty, so yes, every real machine with constant finite memory will complete everything in constant time or loop forever, as it can only be in a finite amount of states.

Luckily, even if our computation models (RAM/TM/…) assume infinite memory, for most algorithms the asymptotic behaviour is describing small-case behaviour quite well.

But not always, e.g. InsertionSort is an O(n^2) algorithm, but IRL much faster than O(n log n) QuickSort/MergeSort, for n up to 7 or so. This is why in actual programs hybrid algorithms are used.