My french is a bit too rusty to understand the justification. 😭

oh my, van damme is a softy with bad math skills, but I won't tell him that (because he can still kick my ass)

That never occurred to me! Unfortunately, you don’t get very far with mathematics if you don’t accept that particular axiom.

(now I went down the rabbit hole of https://en.wikipedia.org/wiki/Group_(mathematics) )

Unfortunately, she couldn’t explain the problem to me (or more likely, I couldn’t understand the explanation), and it ended up with “you just have to accept it” (my first introduction to axioms!), which led me to believe that mathematics was essentially hokum for a while.

my algebra teacher on university said that we should have gotten group theory before learning to do calculation. Technically correct, but infeasible.

I encountered another teacher once, who said he always started with division before addition, subtraction and multiplication. He’d bring a box of apples to class, and slice them until everyone got it (and were stuffed with apple slices).

He swore that kids intuitively understood division and you just had to hook the understanding up to the numbers.

Hahaha cool. I would say that addition/subtraction would be easiest to understand

I have a book about the number 0. In history this number came relatively late. In education it comes relatively soon.

I remember having troubles with negative numbers

I actually had a sort of integer wrapping semantics in my head for a long while, e.g. 0 - 1 is the largest number in existence

I learned fractions (like 0.5) because of a misprint in the text book, my brother explained how it worked

they explained negative numbers to use by adding blocks of cold ice to hot soup so while adding things the temperature still got lower

Ugh, yeah, negative numbers. That was when it started to get surreal.

But the soup explanation is intriguing, albeit for the volume increasing rather than decreasing.

Knowing myself at the time, I would probably get hooked on that (substances) even if I was told to focus on the temperature.

Yet, for some reason, derivation and integration came particularly easily to me. ¯\(ツ)/¯

the + C part with integration came to me only when I was minor’ing in mechanical engineering

before that, I was like, teacher told me to add + C when doing integration

I think credits and debits (or IOUs) would be a good first example to introduce negative numbers, myself. Not the only one, but something people can wrap their heads around.

It helps motivate why adding a negative (an IOU) is like subtracting a positive. And why subtracting a negative is like adding a positive.

I agree.

my abstract reasoning was just not mature enough when I was 13

Weren’t credit and debit columns invented specifically to avoid negative numbers on grounds of being objectively evil?

Certainly in the history of thought, negative numbers were I think at one time considered as odd/strange as imaginary/complex numbers were later regarded.

And they are certainly strange in that they make no sense for counting or measuring the normal kinds of things numbers were originally used for.

its funny how that sounds strange now right

I think of numbers and math as tools/technology to achieve human goals, and like any other kind of tools/technology, later improvements are often discovered and become widespread. Given that they are tools of thought, they require careful motivation and explanation in order to get past the often-initial reaction of "that's nonsense!"

but; there are many things we find ‘normal’ that are strange in the same amount of time