The fundamentals of math takes like 700 pages before it gets to 1+1=2

You blew right by creating the universe first. Your apple pies probably come out terrible.

Can you really talk about 1 or 2 before giving a proper set-theoretic construction of the natural numbers?

Come on, that's way too complex. But how can one count to 10 if they don't know what base to count to 10 in? We should definitely teach them bases first.

Base 11, base 12, and base 16 are all better number systems to teach first imo. A prime number has some benefits when it comes to fractions, but so does a number like 12 which is divisible by many other numbers. Base 16 is useful as you can easily convert between that and the other bases of powers of 2.

You can literally take a class on Complex Analysis. Turns out that those "small" modifications have huge ramifications. They add a ton of extra structure to the real numbers which can be exploited, particularly if your problem can be expressed in terms of sines and cosines, or if your problem lives on a plane.

For example, complex differentiability is much more stringent than real differentiability, to the point that the existence of one complex derivative implies the existence of all of them! Furthermore, you have to be really careful extending the classic functions to the complex numbers. Typically, you either end up with a multivalued function, or you have to pick a specific branch that is single-valued.

If you want to learn more, Theodore Gamelin's Complex Analysis book is a good place to start. But to read it, you'd really benefit from a background in vector calculus. For a more "practical" but still detailed account of complex variables, check out Complex Variables and the Laplace Transform for Engineers by Wilbur LePage, which just assumes basic calculus.

Is there much beyond i^2 = -1, z = a + bi, and e^iθ = cosθ + isinθ

What does electric current "i" have to do with the glorious imaginary unit j ?

This post was brought to you by Electrical Engineering Gang.

!In electrical engineering, we use the letter j instead of i because historically, i is reserved for electrical current. Gamelin uses i in his book ~~which is wrongthink~~, but LePage uses j. !<

We're on Lemmy, who the fuck here isn't annoying‽

Using the word discovered erases the fact that the indigenous peoples were there first, by thousands of years, and that they're all people of equal humanity to columbus.

Trying to insist that genoese serial child rapist is the discoverer of jack shit is literally telling indigenous folks "our bottom of the grease barrel worst still count more than your most important."

As for the norse, is it any wonder everyone forgets about them when even they forgot about it in the intervening centuries. They literally thought the chick who lead the second expedition was a fictional character meant to represent how batshit insane pagans were before her cool younger brother convinced everyone to be nice and christian instead.