Recent content by letmeknow

I got 4 equations, x^2 +yz=1 xy+yw=0 zx+wz=0 zy+w^2=1. How do I solve this now?

I think the question is fine, we have 4 cases to consider. CASE 1: Socko is the one telling the truth. Then Lefty killed Sharky is the truth. But if Socko is the only one telling the truth, then the others must be lying. So Fats (who is lying) says that muscles didn't kill Sharky, ...thus...

Then I'm not so sure that any book will assume Topology. Even in Rudin's Intro treatment of analysis he devotes 1 of 9 chapters to Topology (Rudin's treatment is known to be difficult for most). Choose any book that has a chapter on topology in it and start working through it. If the...

By rigorous class on analysis, which do you mean. I've encountered 2 classes that are called analysis (at my university it is 4 classes, 2 sequences). There is the "analysis" which is proving the theorems from calculus which uses books like "Understanding Analysis" by Abbott and "Principles...

Proposition. A polynomial of degree 2 or 3 over a field F is reducible iff it has a root in F. Tell me if I'm on the right track... I see that x^4 + 3x^2 + 2 is reducible (x^2+1)(x^2+2) but has no roots in Q. This serves as a counterexample to the proposition if states for polynomial up...

A complete graph G on n vertices is a graph that has an edge between any two vertices, no matter which two you pick. The complement of G is a graph of n vertices and is constructed by drawing the n vertices on the paper and then filling in the edges that are not present in G. Which edges are...

That's a great point. Thanks.

I have a question about this. If first we ignore the part about the sums and just consider the points and their distance from the previous terms, do these never approach a particular value on the circle? I see that it is Cauchy in a complete space so it must converge, I thought. It does seem...

Could you expand on this a bit? I like most of the subjects I've encountered so far in a pure masters program (algebra,analysis,topology) and I have studied some set theory also. I have heard that it is hard to publish in this field also, as you said. If one were to study this in a Phd...

I am not sure. I don't have much experience with L'Hospital's Rule so I will look it up.

Homework Statement This should be easy but I can't find why. Why is the following true for 0<x<1, \lim_{n \rightarrow \infty}nx(1-x^2)^n = 0 Homework Equations The Attempt at a Solution I understand why (1-x^2)^n goes to zero, but the nx part is not bounded and seems to...

sin(x) oscillates between -1 and 1. Check on the TI. Also, sin(nx) , such as sin(3x) , just increases the frequency I think. You can graph that too. It just squooshed the oscillations closer to the y-axis. So they are still in between -1 and 1.

So can every function be represented as a Fourier equation? And one more, are we going to finally say that every function is integrable?

Homework Statement My book presents the Riemann-Darboux integral. It has a small supplemental section on the Riemann integral. Then a later section on the Riemann-Stieljes integral. Then a later chapter on the Lebesgue integral. A supplementary text that I have has a section on...

Sorry about the question. I'm worse with words than math, and you know about my math skills Dick. I see that a law like lim[ f(x) + g(x)] = f+g, might confirm this. I usually take this law in one direction -->. But going the other direction atleast partly justifies what I was asking.