M4TH3M4T1C5 - let's prove .99999.... != 1 - The Something Awful Forums

The Something Awful Forums > Discussion > Serious Hardware/Software Crap > YOSPOS > M4TH3M4T1C5 - let's prove .99999.... != 1

Malcolm XML: Aug 8, 2009; I always knew it would end like ｔｈｉｓ．

Widdiful posted:

my fav part of maths is counting up mad stacks of ca$h

# ¿ Sep 13, 2014 00:56

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# ¿ May 19, 2024 19:22

Malcolm XML: Aug 8, 2009; I always knew it would end like ｔｈｉｓ．

math is gay

im math

im gay

# ¿ Oct 28, 2014 22:35

Malcolm XML: Aug 8, 2009; I always knew it would end like ｔｈｉｓ．

Dixie Cretin Seaman posted:

if you like the geometric approach to complex numbers, the book "Visual Complex Analysis" (whose full PDF seems to be the 2nd hit for the title on google, just sayin') goes through most of classical complex analysis this way. it's impressive how far the author gets with mostly geometric arguments.

i would flip what the link above says, though. instead of saying all numbers are really imaginary i would say complex numbers aren't really numbers, in the usual sense. they're a set of rotation and scaling operators in 2 dimensions that happen to share enough important algebraic properties with traditional numbers that you can treat them like numbers for the sake of many computations.

if you're willing to drop multiplicative commutativity there's a 4-dimensional extension of complex numbers called quaternions, and in 8 dimensions there's a non-associative extension called octonions. it's been proven that those are all the possibilities for defining sets like these (extensions of real numbers that let you add, multiply, and divide by non-zero elements).

Visual Complex Analysis is the greatest math book ever written

Complex Analysis is super nice and far more interesting than real analysis and ends up explaining tons of things in applied math. Fourier series, function approximation and poo poo are just trivially done in C

# ¿ Oct 31, 2014 16:26

Malcolm XML: Aug 8, 2009; I always knew it would end like ｔｈｉｓ．

El Wombato posted:

Yea and interpolation in quaternion space actually works pretty well unlike a lot of other representations.

yeah there are other charts of SO(3) that are just as good, like mobius rotations on the riemann sphere but quaternions are nicer i guess?

# ¿ Oct 31, 2014 16:31

Malcolm XML: Aug 8, 2009; I always knew it would end like ｔｈｉｓ．

Greed is eternal posted:

Now how do I extend the zeta function to s<0?

\zeta(-1)=\sum_{n=1}^\infty n^{1} = 1+2+3+...=1/12

\zeta(s) = 2^s \pi^{s-1} \sin \left(\dfrac{\pi s}2\right) \Gamma(1-s) \zeta(1-s)

# ¿ Nov 1, 2014 21:59

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