/sci/ - Science & Math

Lets say we want to order a group of things.
If we have, say, three of them, the easiest way to order them would be to assign the numbers 1,2,3 respectively to the things. So we can order the alphabet, for example, by assigning 1 to a, 2 to b, 3 to c, etc. Then you can compare them with < and > and have it make sense. For example a < c, and e > d.


Now lets say you have an infinite number of things. For example, all possible words where letters are strictly decreasing, so you can have an 'a' after a 'b' but not a 'b' after an 'a'. Then valid words are dddddccba, ba, a, bbbbbbbbbba, zbba, and other things like that. Then, if you sort them in alphabetical order, you can compare them like in the single letter case. It's obvious that, for example, a < aa. And that aaa < aaaaaaa. And that aaaaaaaaaaaaaaaaaa < b.

Pure math general. Ask stupid questions! Win girls' hearts with your prowess in analysis! Convince each other that we will be not be unemployed after we finish school! Brag about your superior intellect!

To start off with a problem for people to attempt. Feel free to ignore it:
Show that the group <span class="math">\langle x^{-1}yxy^{-1}xy = yx^{-1}yx[/spoiler] is nonabelian.
I'll give a hint of necessary.

>>4503953
And what makes you classify it like that?
<--This guy, by the way, classifies the main areas of math as Geometry, Algebra, and Analysis. However, it is worth noting that he is not truly classifying the "areas of mathematics" but rather "types of mathematical techniques". There are many areas of math, obviously, and it is silly to force them all into those three areas, but you almost always are using techniques from those areas.

Its also worth mentioning that theres a 50 page or so section on complexity theory in that book.

if you don't own this book you don't know SHIT about mathematics

>>3903623
oops, forgot the pic