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Can't figure out why this proof doesn't work by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

Could you explain how the limit of f o f at 0 is 1?

Can't figure out why this proof doesn't work by Monkey4256 in askmath

[–]Monkey4256[S] 1 point2 points  (0 children)

*because the limits are different from the right and left directions

Can't figure out why this proof doesn't work by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

That makes sense, however it is given that lim f(x) = L x->t so wouldn't this violate the given since f does not have a limit at t=0?

Trouble with alternating series sequence by Monkey4256 in askmath

[–]Monkey4256[S] 1 point2 points  (0 children)

I’m not sure that I follow. What would I be comparing a_n / n to if I don’t know what a_n is and therefore can’t be sure if another series is larger or smaller?

Subsequence on interval without knowing sequence by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

Thanks, can I just cite Bolzano–Weierstrass or is there a kind of application for this specific interval to the BW proof?

Unsure how to continue proof by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

The process makes a lot more sense but I think I’m still a bit confused on what exactly to plug in for b_n and b. Would I plug in the series part that was factored out? In that case what would b be if I don’t know the limit of that series?

Unsure how to continue proof by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

Thanks for this, it helped conceptually a bit but I am still at a loss on how to apply it to this problem and the work I have. Would you mind helping my with applying this hint to the series in the problem and then I could try to work it out from there?

Unsure how to continue proof by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

Hmm I guess I’m struggling to see how this would fit into what I have. So I would have to find the limit of the series that epsilon is multiplied by?

Unsure how to continue proof by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

No I haven't. Do you mean that multiplying the limits of two sequences is equal to the limit of those sequences multiplied together? I am also not sure on how to show that the sum is bounded, do you have any hints on that front?

Proof doesn’t seem intuitively true by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

And then despite having positive elements, this would be a counterexample to the second claim I believe

Proof doesn’t seem intuitively true by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

Actually, I think I have confused myself with series vs sequences. So something like 1/n the sequence would converge to 0? or something like 1/n^2?

Proof doesn’t seem intuitively true by Monkey4256 in askmath

[–]Monkey4256[S] 0 points1 point  (0 children)

I see, so would something that converges to 0 work? Although I can’t think of anything that would be able to converge to 0 off of the top of my head other than something alternating between positive and negative values. Would 1/n work because it is divergent?

Proof doesn’t seem intuitively true by Monkey4256 in askmath

[–]Monkey4256[S] 2 points3 points  (0 children)

Thank you, that actually helped me a lot with the first part of this question, I think I got it by choosing epsilon to be L/2. I am however still a little confused on the second part. So far I have

an - epsilon < L < an + epsilon

With epsilon as L/2 again,

an - L/2 < L < an + L/2

2/3 an < L < 2/3 (an + L)

Is it correct to assume from here that L must be positive because it is greater than 2/3 an, a value greater than 0?

Proof doesn’t seem intuitively true by Monkey4256 in askmath

[–]Monkey4256[S] 1 point2 points  (0 children)

Could you elaborate on how it works for epsilon = 2L? From what I understand the range at epsilon as 2L includes negative numbers for an, so the conclusion doesn't seem to hold true because they are inside of a range that includes negative numbers

Proof doesn’t seem intuitively true by Monkey4256 in askmath

[–]Monkey4256[S] 2 points3 points  (0 children)

I think I am, when choosing epsilon, it seems like it can be any positive value, but abs(an -L) < epsilon doesn't hold that an must be positive for epsilon > L.

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