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...
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!