Thread replies: 13
Thread images: 2
Thread images: 2
Anonymous
What did they mean by this? 2017-01-22 12:33:20 Post No. 8620030
[Report] Image search: [Google]
What did they mean by this? 2017-01-22 12:33:20 Post No. 8620030
[Report] Image search: [Google]
File: WildTheoryAbstractAlgebra.png (697KB, 1048x541px) Image search:
[Google]
697KB, 1048x541px
I was watching today's Wildberger video and at some point he decided to play the game of the reals. He decided to solve a problem in complex numbers using the usual methods taught at universities instead of his patented method.
This involved calculating an angle and for that he needed to compute the arctan function of [math] \frac{12}{5} [/math] and he used used the series
[math] \arctan(x)=x-\frac{x^3}{3}+\frac{x^5}{5}-\frac{x^7}{7}+\dots [/math]
But then he said that actually this series diverged for the number [math] \frac{12}{5} [/math]. But that makes no sense. The arctan function actually has a value then. So what gives? That series is BULLSHIT.
I, for a moment, disbelieved Wildberger (I shouldn't have) and decided to prove such a thing. That the series would diverge. I did it on paper, got my Calc 2 notes out. And did it. And it is true.
Is this one of the many flaws with real analysis? How come this is just coming to light? Why is Wildberger the only person to say this? Why is everyone else hiding the fact that real analysis doesn't work?
Here is the video and the part where he says this:
https://youtu.be/Snq7UJT8EWg?t=12m27s
>>
>>8620030
>try to sum series outside the radius of convergence
>holy shit why is it diverging
>>
>>8620046
>radius of convergence
Nice damage control
>>
>>8620030
It doesn't converge to a rational number
Therefor it diverges.
too lazy to actually check the video
>>
>>8620030
Of course it diverges, use the ratio test
>>
>>8620078
I already proved it. I ddn't use the ratio test though.
What is curious is that when someone tells you to compute arctan, what you or the calculator uses is this series. AND THIS SERIES IS FLAWED.
There are so many flaws with real analysis it is unbelievable. We should stop this farce right now. In the video Wildberger solved the same problem using only rational numbers and functions. It is amazing.
>>
>>8620088
I sense this is bait, but just in case you're not baiting, you can compute arctan numerically as the integral [math]\arctan x = \int_0^x \frac{dt}{1+t^2}[/math]
>>
>>8620088
>use series outside radius of convergence
>it does not work
>waah real analysis doesn't work!
Retard
>>
>>8620094
he called the idea of radii of convergence "damage control"
of course he's baiting you doofus
>>
>>8620088
>what you or the calculator uses is this series
Citation needed
>>
He shouldve not used it becouse maclaurin series of arctan doesn't converge values over 1. He could have used it if it converged but it did not.
>>
>>8620088
"Flawed" real analysis can solve every problem of that kind and wildberger's approach gives answer to only a couple, or actually to almost none of such problems. The difference between real analysis and wildberger's bs is that real analysis always gives you an answer, just not always in nice or neat form, and wildberger just says "I don't like this solution, it's too hard and doesn't have nice representation in my arbitrarily chosen notation, so let's just say it can't be solved".
>>
>reject reals that can be constructed with just straight edge and compass
>accept imaginary numbers which don't exist in the real world and have no direct relation to the real world whatsoever
What's wrong with him?
Thread posts: 13
Thread images: 2
Thread images: 2