Recent content by ironspud

Nevermind. I just spoke with my professor. Seems I was just over thinking everything. Still, if anyone would like to provide some insight to part (b), I'd appreciate it.

Homework Statement Okay, so here's the problem: (a) Let U be a universal set and suppose that X,Y\in U. Define a relation,\leq, on U by X\leq Y iff X\subseteq Y. Show that this relation is a partial order on U. (b) What problem occurs if we try to define this as a relation on the set...

Homework Statement Find f^{-1}(x) if f(x)=x^{2}-8x+8 and x\leq4 The Attempt at a Solution I set y=x^{2}-8x+8, and then switch y and x to get x=y^{2}-8y+8. I then try solving for y, but I end up with y's on both sides of the equation: x=y^{2}-8y+8 x-8=y^{2}-8y x-8=y(y-8)...

Yeah, I figured there was no problem in the substitution, though, maybe I should have provided the reasoning behind it in the proof. Oh well. Anyway, thanks again.

Thanks dynamicsolo. And, yeah, I get the substitution by knowing \frac{1}{2\sqrt{n^*}+1}<\epsilon. Solving for epsilon, [\frac{1}{2}(\frac{1}{\epsilon}-1)]^2<n^*. And since n\geq n^*>[\frac{1}{2}(\frac{1}{\epsilon}-1)]^2, then...

Hi, Just hoping someone could check my work and point out any errors, if any. Homework Statement Consider the sequence {a_n} defined by a_n=\frac{n}{2n+\sqrt{n}}. Prove that \lim_{x\to\infty}a_n=\frac{1}{2}. (Do NOT use any of the "limit rules" from Section 2.2.) Homework Equations A...

If you look at a truth table for a conditional statement such as P\rightarrow Q, you should find that the only time this statement is rendered false is if the antecedent (the first part, P) is true and the consequent (the second part, Q) is false. So, what does that tell you about your...

No. I don't think so. I mean, I get what you're saying. I just don't think I have the tools to prove something like that - i.e, I don't know how to represent or manipulate statements like that symbolically.

Yay. Thanks. Question, though. What would be the difference between what I said I was asked to prove - i.e, "arbitrary unions/intersections" - and what I was actually asked to prove? I know that's probably a really stupid question but, like I said, I've never taken any sort of...

Hi, So, I was assigned a problem in my Intro Analysis course that involves proving, by induction, that the set A minus some arbitrary number of intersections of the sets B_{j} is equal to some arbitrary number of unions of A minus the sets B_{j}. I've written out a proof, but I'm not too...