Thanks Dick, Cauchy + Completeness clarified it. I noticed that the problems in this book reference things from all over the place. And many thanks Ivy for taking the time to set everything straight. Very appreciated!
Homework Statement
From Introduction to Topology by Bert Mendelson, Chapter 2.7, Exercise 8:
Consider the subspace (Q, d_Q) (the rational numbers) of (R, d). Let a1, a2, ... be a sequence of rational numbers such that \lim_{n} a_n = \sqrt{2}. Does the sequence converge when considered...
Is there a collection somewhere of particle interaction descriptions? For example, if I'm wondering what an electron-positron interaction does, what website can I type "electron positron" into and get back a handful of Feynman diagrams of relevant interactions?
If that's too idealistic, is...
Thanks for the recommendations. Is it possible to make an angled arrow?
I think I'll stick to CorelDraw for the time being. I could probably make a simple SVG-to-picture converter program, but I'm not sure how much it's worth the trouble.
Actually there are obviously LaTeX picture...
Homework Statement
From Introduction to Topology by Bert Mendelson, Chapter 2.4, Exercise 8:
Let R be the real numbers and f: R -> R a continuous function. Suppose that for some number a \in R, f(a) > 0. Prove that there is a positive number k and a closed interval F = [a - \delta, a +...
That's hilarious. I was thinking that if we define an open ball of radius d(a,b)/2 about each point, then the neighborhoods wouldn't intersect. But I wasn't sure I could generalize this from R^2. Thanks.
Here's an attempt at a proof:
About each point a and b, define an open ball of radius...
Homework Statement
From Introduction to Topology by Bert Mendelson, Chapter 2.4, Exercise 6:
Let a and b be distinct points of a metric space X. Prove that there are neighborhoods N_a and N_b of a and b respectively such that N_a \cap N_b = \varnothing.
2. The attempt at a solution
OK...