Recent content by TupoyVolk

Thanks for your reply. I don't think I am 'so smart.' I guess I implied that, I'm sincerely sorry. I think all humans are pretty much the same level of learning capability (excluding those with mental problems) :). I'm not assuming success. I think anyone trying to find out something unknown...

Here's my battle plan: 1: Learn (the principles) of verified models for fundamental physics. QFT, GR, Standard Model, etc. 2: Try to think of what I don't know and what I'd like to experimentally test.I think I'd prefer to get a regular job and research physics in my free time, rather than be...

Perfect. I am incredibly satisfied, really. Thank you for sharing these ideas with me!

So would it suffice to choose this delta for f(x) = x2; δ = ε|(f-1(L+ε)-a)/((L+ε)-L)| δ = ε|(f-1(L+ε)-a)/ε| δ = |(f-1(L+ε)-a)| δ = |(L+ε)0.5-a)| ie: choose it for the highest value x can be so that such that |f(x)-L|<ε Is that an OK 'choice' or does it have to be more specific? ∀x...

I see, thank you! So what's the trick to get a fixed delta for an f(x) = xn Upper bounds of x; ... take what would be "the smaller" δ (ie for x = (L + ε)0.5) :/? Excuse my niavity. It is not on the current course, I'm just 'annoyed' to only know how it works for straight lines. Edit: Looked...

How can you have a fixed delta if the epsilon is fixed and the function is a curve? You could easily choose the smaller delta if you wanted it to be 'within' the ε.

eh... why? δ = ε|(x-a)/(f(x)-L)| always returns the desired ε interval, though. It's the exact same as saying when f(x) = L ± ε, what is x. Where's the problem with this? It makes sense that δ should depend on x as the graph is not straight Here is an example choosing ε = 1, for...

durr

So the general tactic for straight lines: f(x) = 2x Show by epsilon-delta definition of limit, as lim x->2, f(x) tends to 4. let, ε>0, and choose 0<δ<ε/2 (|x - 2|<δ)→ |f(x) - 4| = |2x - 4| = 2|x - 2| < 2δ < ε No problem, but what about for a parabola? g(x) = ax2 for some a in R. Show as lim x...

Sorry, it's only self study at the moment. I am in a theoretical physics course at the moment, did 3 years experimental; didn't like it, wanted better understanding. Unfortunately, if I specifically want to go into mathematical physics, it will have to wait until masters. I'm just deciding what...

Thanks for the reply! I did a few more chapters of Introduction to Set Theory. You're totally right. I understand it is necessary to prove every single obviously-intuitive things, but they seem pedantic for someone with my goals (I'd like to end up somewhere 'mathematical physics-y'). I think...

I recently learned predicate calculus from Schaum's Outline of Logic. in this sort of form: In addition to refutation trees, however; pfff, refutation trees. I'm reading "Introduction to Set Theory," Hrbacek, Jech. I'm a little "annoyed" by the informal proofs. [FONT="Arial Black"]Are any...

Cheers! Much appreciated.

Gah, I'm pretty sure from clicking the linked definition of tensor on here, I got the answer :P Tensor of rank 1 = V^a*e_a Components of a tensor of rank 1 = V^a. Oui?

"The components of a vector change under a coordinate transformation, but the vector itself does not." ie: V = a*x + b*y = c*x' + d*y' Though the components (and the basis) have changed, V is still = V. Question 1: Is that right? (I'm assuming so, the main Q is below) Tensor rank...