/sci/ - Science & Math

>>8557108
woops, forgot to apply [math]g [/math] for the way back:

the
[math] A_{2k}=[\frac{1-3^{-2k}}{2},3^{-2k}+\frac{1-3^{-2k}}{2}] [/math]
[math] A_{2k+1}=(\frac{1-3^{-(2k+1)}}{2},3^{-(2k+1)}+\frac{1-3^{-(2k+1)}}{2}) [/math]

[math] M= \{ (\frac{1-3^{-(2k+1)}}{2},\frac{1-3^{-2(k+1)}}{2}), (3^{-2(k+1)}+\frac{1-3^{-(2(k+1)+1)}}{2},3^{-(2k+1)}+\frac{1-3^{-(2k+1)}}{2})\mid k\in \mathbb{N}\cup \{0\} \} [/math]

[math] N=\{ [\frac{1-3^{-2k}}{2}, \frac{1-3^{-(2k+1)}}{2}], [3^{-(2k+1)}+\frac{1-3^{-(2k+1)}}{2},3^{-2k}+\frac{1-3^{-2k}}{2}] \mid k\in \mathbb{N}\cup \{0\} \} [/math]

[math] \varphi(x)= \begin{cases} (x+1)/3 & x \in N \\ 3x-1 & x \in M \end{cases} [/math]

>>8523771
your lack of convinction is exactly why no one will take you seriously

>>8439573
i know a lot of people who took those classes, very well could have seen each other

which 1st year res? i was in chown

>>8417360
fun-guy <--

>>8396968

np

>>8384953
lurk more brainlet

>>8376605
http://thatsmathematics.com/mathgen/ might do what you want

50/50, either it is or it isn't

>>8352435
d(x,y)^2
=(x1-y1)^2+(x2-y2)^2
=(x1-z1+z1-y1)^2+(x2-z2+z2-y2)^2
= (x1-z1)^2+(x2-z2)^2+(z1-y1)^2+(z2-y2)^2 + 2[(x1-z1)(z1-y1)+(x2-z2)(z2-y2)]
=d(x,z)^2+d(z,y)^2+2[(x1-z1)(z1-y1)+(x2-z2)(z2-y2)]
<=d(x,z)^2+d(z,y)^2+2[sqrt((x1-z1)^2+(x2-z2)^2) sqrt((z1-y1)^2+(z2-y2)^2)]
= d(x,z)^2+d(z,y)^2+2d(x,z)d(z,y)
=[d(x,z)+d(z,y)]^2

for the inequality step you use cauchy's inequality

>>8258558
>What can we do at this point to mitigate the damage?
nothing, it's too late

>What is the average citizen's life expectancy after the crash?
you realize were going the way of the dino's right?

People still post middle school homework threads on /sci/?

You really came here just to brag about your Ph.D?

>>6846326
I picked Queen's mostly because you have a general first year program before deciding what you want to specialize in so I could put off picking a major for a bit longer (wasn't sure what I wanted to do at the end of high school). I picked math after going through first year honours calc, it was the first time I was both very interested and very challenged by a course (my high school was a joke). I'm in fourth year now.

>>6846330
We have complex and two real analysis courses but the only topology I've ever learned was in the real analysis classes, we have no coures devoted to point-set or algebraic topology even for graduate students. I basically ran out of pure math courses to take for my final year now and had to resort to taking graduate courses. Professors are accomodating though, especially for creating reading courses.