Recent content by magic88

Thank you, micromass! I understand now. Thanks for getting me on track :)

Thanks for your reply, micromass. I'm drawing a blank on how to incorporate the well ordering principle into proving it. It seems like I could just use the ceiling or floor function to show x <= z <= x+1. Do I let the let the ceiling of x be the least element of a set of z integers in the...

Homework Statement We just started learning about supremums and infimums in my math proofs class. I am having trouble with the following question: Let x, y be real numbers with y - x > 1. Prove that there exists an integer n such that x < n < y. Hint--use the well ordering principle...

Thanks very much! Your tip about writing (a) and (b) in terms of the first sum really helped... I don't know why I didn't think of that. I got: (-1)^{n+1}\frac{n^2+n}{2}

Homework Statement This is a proof problem in the mathematical induction section of my textbook. I am having trouble with question (c). Result: 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6 for every positive integer n. (a) Use the result to determine the formula for 22 + 42 + 62 + ... + (2n)2 for...

Thank you.

Hi there, I am learning about quadric surfaces in my second year multivariable calculus course. I would like to know how most people would identify (find the name of) a quadric surface if they had the equation. We only need to know 6 different quadric surfaces, so should I ... (a)...

Hi there, I just have a quick question about what "S36°E" means. Here is part of my homework question: A boat sales south with the help of a wind blowing the direction S36°E ... Does it mean 36° East of South or 36° South of East? Thanks in advance!