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...
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...
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...
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...