Recent content by A.MHF

Thanks guys, that was super helpful!

Homework Statement So I've read a lot about this but still can't figure what's going on. I understand that to find the error of approximation all we have to do is: |E(x)| = |f(x)-Tn(x)| But what about M*(xn+1/(n+1)!) What's the point of this? and why does it have to be greater than or equal...

Oh, I don't how I missed that, feel stupid for asking haha. Thanks.

Homework Statement So I was doing this problem in Munkres's Topology book: Determine whether the statement is true or false, If a double implication fails, determine whether one or the other of the possible implications holds: A ⊂ B or A ⊂ C ⇔ A ⊂ ( B ∪ C ) Homework Equations - The Attempt...

Thanks, these were my thoughts at the beginning but I wanted to make I'm investing my time in something useful. My background is wide, I have deep knowledge of calculus, discrete mathematics, matrices, some knowledge in Set Theory, and a bit of real analysis and number theory. I'm sure I have...

A few months back I bought Spacetime Physics by Taylor and Wheeler, I haven't read it, but I was planning to. Generally, I do love physics especially the math part. I'm also self-learning some courses in mathematics and I was wondering if it would be helpful to me to also start learning some...

Oh I see. So I should define p=q+1 in which the corresponding real number is p={x<ℚ:x<p} such that p≠s. And s⊂q → s⊂p, thus we proved that there is a a real number p such that it's greater than q yet doesn't satisfy p≤s, therefore ℝ has no upper bound.

Thanks, that was helpful. Regarding the exercise (in the same page), I constructed this proof, what are your thoughts? Assuming there was such a number s such that r≤s, for all r∈ℝ then since s∈ℝ, there is q such that q∉s. Now suppose that p=q+1. let q be the real number corresponding to q and p...

Yeah that's what I meant when I said unless q is greater than the real number s,since it's a Dedekind left set, it won't include it. But still, why are we trying to prove that UA≠ℚ?

Homework Statement I'm reading Goldrei's Classic Set Theory, and I'm kind of stuck in the completeness property proof, here is the page from googlebooks...

I see. Just to be clear, is this right: Let's say there is are sets A:{1,2,3} and B:{4,5,6}. The axiom of pair would tell me that this set exists: {{123},{456}}. The axiom of union would tell me that this one exists: {1,2,3,4,5,6}.

The first one is a set whose elements are A and B. The second one is a set whose elements are the elements of the sets A and B. Is that correct?

So I've been learning Set Theory by myself through Jech and Hrabeck textbook, and I'm having trouble understanding some axioms. 1. Homework Statement What exactly is the difference between the axiom of pair and axiom of union? From what I understood, the axiom of pair tells us that there is a...

Thank you for your answers, you were helpful.

I know this sounds like a weird question, but I'm interested. So I've always loved math, especially pure mathematics. I spend a lot of time reading about theorems, mathematical proofs, and I try to come up with my own proofs. Recently I had the idea that maybe I can spend my time reading some...