Recent content by nomadreid

The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in...

As a longtime mathematics secondary school teacher, I know the solution to this situation if one doesn't want to admit that one doesn't know: "Excellent question! That's your homework assignment for tomorrow."

Thanks very much, PeroK. That is very helpful The idea of only considering small delta and epsilon is completely reasonable. (It makes me think that the proofs could be adapted to a non-standard analysis approach in requiring that delta and epsilon are infinitesimals.)

Thanks very much, Gavran. As far as I understand, you are saying that one derives a delta based on both cases, and then pick the smallest of the two? I will work through some cases this way; it is an interesting approach that was not explicitly presented in any of the examples which I have seen.

Thanks, Gavran. If I get this straight, to set b you can use the bound k for |x-a|, allowing you to set delta in terms of epsilon and b. But then where does the bound delta<k come from in the last step, and what role does it play?

Thanks, pasmith. I am wondering about the apparent difference between your explanation and that of Gavran (post #10) who told me (if I understood correctly) to eliminate the delta in the premise of the inequality in your implication.

Thanks very much for the correction and explanation, Gavran. Your correction leaves me a little puzzled, in that all the expositions and examples I have read derive the relationship between epsilon and delta by assuming that |x-a|<delta. That is, they factor the |f(x)-L| =h(x)*|x-a|...

Thanks for the reply, WWGD, but my question is a bit more basic. In a nutshell, I am asking whether the process [1],[2],[3] in post #5 is a proper explicit explanation of why the last step in the typical epsilon-delta proof of a limit is valid: that is, when you assume a bound for delta at the...

Thank you very much, Borek. Your drawings are very helpful, and a bit of the fog is starting to lift. Let me see if I have this straight. The idea is to look at the two carbon atoms on each side of a double bond, one regards the group with the highest priority on one side, and then the group...

(Edit: Forgot tags; couldn't go back and re-insert. So, tag: stereochemistry.) The following 3D visualizations are taken from https://pubchem.ncbi.nlm.nih.gov/compound/4Z_-5_6-dichloro-1_4-hexadiene#section=3D-Conformer For (4Z)-5,6-dichloro-1,4-hexadiene So I am not sure how to...

fresh_42, thanks a lot! This looks like it will be very useful.

Thanks very much, pasmith. First, I apologize for writing out delta, etc., but I have attempted to type it with \delta as seems to be indicated in the "LaTeX Guide" on this forum, but without the required results. I also tried ##\delta and \delta\ without success, and even [itex]\delta. Sorry...

Thanks for that, mjc123. (Oopso:).) I have edited it.

In the last step in a standard technique for doing an epsilon-delta proof of a limit (in which one takes the minimum of two possible functions delta of epsilon) the presentations I have found usually have a logical jump that I am not sure how to fill in, despite staring at examples. The general...

Thanks very much, mjc123. Super. Excellent information, followed by sage advice that I will indeed follow.