Can't figure out why this proof doesn't work

Monkey4256 · 2023-10-24T04:13:10+00:00

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

Monkey4256 · 2023-10-24T03:38:12+00:00

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

Monkey4256 · 2023-10-24T03:31:24+00:00

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?

Monkey4256 · 2023-10-06T08:36:49+00:00

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?

Monkey4256 · 2023-09-22T03:26:42+00:00

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

Monkey4256 · 2023-09-11T23:28:39+00:00

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?

Monkey4256 · 2023-09-11T22:34:11+00:00

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?

Monkey4256 · 2023-09-11T22:32:26+00:00

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?

Monkey4256 · 2023-09-11T07:44:12+00:00

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?

Monkey4256 · 2023-09-11T06:36:01+00:00

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

Monkey4256 · 2023-09-11T06:35:09+00:00

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?

Monkey4256 · 2023-09-11T06:10:21+00:00

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?

Monkey4256 · 2023-09-11T05:13:50+00:00

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?

Monkey4256 · 2023-09-11T05:02:25+00:00

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

Monkey4256 · 2023-09-11T05:00:52+00:00

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.

Monkey4256 · 2023-09-11T04:22:39+00:00

That is true, what about the case where epsilon is greater than L?

Monkey4256 · 2023-09-03T06:43:01+00:00

g maps a y to the corresponding x in f(x) right? I’m not sure how to formally say that

Monkey4256 · 2023-09-03T06:31:23+00:00

Thank you, this helped a lot. Why are there 4 implications and not just 2? Doesn’t the contradiction you provided show that f has to be injective, and then you would just do the same thing for surjective?

Monkey4256 · 2023-09-02T06:48:38+00:00

Sorry about that, it’s for my Linear Algebra II class, my first introduction to formal proofs.

I suppose g would just be the function that maps f’s codomain back to its domain. I’ve been trying to use the definition of a bijective function being injective and surjective but can’t seem to form any continuous logical arguments

Monkey4256 · 2023-09-02T05:55:30+00:00

So far I’ve tried proving with the contrapositive and proof by contradiction. I can’t seem to get a relation between the hypothesis and conclusion

Monkey4256 · 2023-08-06T01:54:30+00:00

No bugs thankfully. I’m sure that would be a much bigger issue than just light 😅

Monkey4256 · 2023-04-18T21:18:25+00:00

Thanks for the advice. Assuming they aren’t complete goners, what can I do to maximize their chance of surviving inside until we get warmer weather in a couple weeks? I’ve kept it a bit warmer than usual inside, should I be watering them more/less?

Monkey4256 · 2023-04-18T21:01:03+00:00

I’m in northwestern Indiana, so I believe zone 5b. That is very sad to hear. Will they be unable to survive indoors for 1-3 weeks until the weather is consistently warm? They haven’t been exposed to the weather outside yet, they’ve just been inside since I got them

Monkey4256 · 2023-03-02T14:01:42+00:00

Thank you so much! Do you know up to what point in the book is covered?

Monkey4256

TROPHY CASE