/sci/ - Science & Math

>>16008416

>>12786382
Not all equations can be solved analytically. Also OP is a mouthbreather

>>11287140
absolutely based

>>10441495
gold

>>10441624
their conclusions ignore the fact that iq is almost completely genetic. they're homeless because they are dumb, and anything we do for them is a waste of time and resources

>>10412907
But it does need to be fixed anon. the way we teach math is dumb.
Common core is an attempt to teach people how to actually reason their way to the answer rather than perform number art on the paper to magically generate the correct answer.
When you teach these "simplified" "commonsense" strategies you never know what bizarre patterns or techniques people actually internalize
The shit you currently see on the undergrad level as an instructor is just incredible

>>10362347
>>10365825
>>10365833
The worst part is that [math]1 + 2 + 3 + 4 + \dots = -\frac{1}{12}[/math] actually is true... if you, as those who originally drew this conclusion, define [math]=[/math] to mean "is associated with," and it can indeed be proven that that series "is associated with" [math]-\frac{1}{12}[/math] through actually rigorous methods (zeta regularization, integration, etc.).
The thing is, of course, that nobody uses that notation like that, so you get pop-sci/pop-math retards like Numberphile and their audience who read that Ramanujan wrote [math]1 + 2 + 3 + 4 + \dots = -\frac{1}{12}[/math], assume that he actually meant that the divergent infinite series of natural numbers sums to a finite negative fraction, and unquestioningly accept it because they are retards to whom math is indistinguishable from wizard magic.
And the "proofs" they use to justify this "sum" absolutely are unrigorous; you actually can algebraically manipulate an absolutely convergent series term-by-term (for instance, you can fiddle with the infinite series of [math]\exp{\left(x \right)}[/math], [math]\sin{\left(x \right)}[/math], and [math]\cos{\left(x \right)}[/math] to prove that [math]\exp{\left( ix \right)} = \cos{\left( x \right)} + i\sin{\left(x \right)}[/math] because those are all absolutely convergent), but you definitely cannot do that to a series that is anything less than absolutely convergent—at least, you cannot do that and expect to get an actual sum—and you especially cannot do that to a series that is demonstrably and obviously divergent like [math]1 + 2 + 3 + 4 + \dots[/math].
...That said, this does mean you can algebraically manipulate [math]0.999 \dots[/math] like that, since it is absolutely convergent (to [math]1[/math]).
But you can't use that to prove that.

I'd hope that this would end all the retarded comparisons to [math]1 + 2 + 3 + 4 + \dots = -\frac{1}{12}[/math] ITT, but I've learned all too well that there is no stopping retards.

>>10345193
we need more of these