>>16951499
it has though, just that we don't teach those advancements to knuckle draggers at school anymore. Look at yourself. Remember the average high schooler, if you ever even attended. Even basic calculus they don't wanna learn because, quote, "why are there letters, where are the numbers".

>>16951585
You’re confusing algebra with calculus pajeet

>>16951587
No, people make the claim about both, and complex numbers, too. Algebra is already hopeless enough though, you are right. But back on topic, someone like that wouldn't even get the point of SVDs.

>inb4 reee groups and number fields are algebra too
I am making a point about school children, Anon.

>>16951585
I think you could almost teach calculus at the same time as algebra, at least the really basic ideas of it. I feel like little knuckle dragger me would have gotten into math earlier if I had some protocalculus to show me how it relates to the physical world in 9th grade math.

>>16951629
For example, I wouldn't have been smart enough to figure out integration by parts or anything but maybe if they made us graph velocity over time and had us count the squares under the graph to find distance that would have been pretty educational for me.

>>16951499
anon... that's just a formalisation of an infinitesimal. there's nothing insane about it, and it's not a modern concept in itself

>>16951630
that already makes you smarter than the average Anon. You need to understand that people are aggressively ignorant and don't want to be taught what doesn't help then eat, shit or fuck better.

>>16951693
Quote of the year

>>16951693
>eat, shit or fuck better.
Ive literally travelled the world, in circles like a dog, looking for a place to permanently eat (home cooked meals), shit (normally instead resturants), or fuck better (than not). Quarter million miles, the distance to the moon.

>>16951672
theres nothing sane about infinites

>>16951499
Where the fuck did you get the idea from that math hasn't advanced in 200 years

>>16952010
Physics certainly has but not math lol

>>16951499
Math devolved 200 years ago. Lagrange gave calculus the most solid footing there was, is and ever will be.

On a semi related note, dual numbers are just as legitimate as complex numbers. If you believe there is a number that multiplied by itself equals -1, then you shouldn’t have problem with the former.

e2 is just zero

there I solved it

>>16951693
>You need to understand that people are aggressively ignorant and don't want to be taught what doesn't help then eat, shit or fuck better.
Is that bad?

>>16952202
>dual numbers are just as legitimate as complex numbers
Dual numbers do not form a field, they are a far weaker type of "number". Quaternions have the same issue, but being non-abelian is a much less egregious departure.

>>16952681
It doesn’t matter, different tools for different needs. Not every tool needs to be a hammer lol

>>16953135
1) I agree
2) I would say the there is an innate "numberyness" to the rational numbers, and that any departure from it kind of fucks with the resulting structure's character. That said I find it upsetting that the term algebraic number field has a formal definition that excludes the reals without a generalized term for the kind of field that would include them.
3) It's more an aesthetic/vibe issue, not gonna defend it

>>16953205
>I would say the there is an innate "numberyness" to the rational numbers, and that any departure from it kind of fucks with the resulting structure's character.
Hard agree. Are you me?

>>16952202
i mean, they do have zero divisors, while the complex do not, that being said automatic differentiation is a pretty neat feature i must say!

>>16951499
>dual numbers
>>16951672
>anon... that's just a formalisation of an infinitesimal.
This definition could be useful more if you are willing to use a non-classical logic like the intuitionistic one
https://en.wikipedia.org/wiki/Smooth_infinitesimal_analysis
https://publish.uwo.ca/~jbell/invitation%20to%20SIA.pdf

>>16957542
Holy fuck, i meant
>could be made more useful
>if you were willing

>>16951499
>meaningfully contribute to the field
Define what is a meaningful contribution? Math is just, here are some rules, what can we do with it? What if we change the rules? etc