Comment by dan_mctree

There's so much ambiguous context that goes into your average '=', even when just talking about your standard functions on real numbers. You'll see it being used for anything from:

- We've found these to be equal

- We're hypothesizing this to be equal

- These are approximately equal

- These are defined to be equal

- This is a way to calculate something else, whether it's equal is up to your philosophy (a^2+b^2=c^2)

- I'm transforming my function into something else that looks different but is exactly the same

- I'm transforming my function into something else that is the same for some of the stuff I care about (but for example does not work anymore for negative numbers, complex nrs, etc.)

- I'm transforming my function into something else, but it's actually a trapdoor, and you can't convert it back.

- This is kind of on average true within an extremely simplified context or we know it's not true at all, but we'll pretend for simplification (looking at you physics)

- We are trying to check if these two are equal

- This is equal, but only within a context where these variables follow some constraints mentioned somewhere else entirely

- This is equal, but, we're not going to say whether you can or can't replace the variables with functions or whether it supports complex nrs, negative nrs, non-integers, etc.

A lot of this is usually kind of clear from context, but some of these differences are a nightmare if you want to code it out