Recent content by nomadreid

Thanks, fresh_42!

Thanks, fresh_42. I know that it's pure convention, but I am trying to understand the relations between the conventions. What is clear is that ---physicists often use bra-ket <v|u>, linear in the second argument and ---mathematicians often use (u,v) , linear in the first argument, What is...

anuttarasammyak, thank you for pointing out that I should have made precise that I was referring to complex vector spaces. I have edited the question accordingly. However, the question still stands.

First, I need to check that I have the 3 notations correct for an inner product in finite vector spaces over a complex field; v* means: given the isomorphism V to V* then: (a) physicists and others: (u,v)=v*u ; linear in the second argument (b) some mathematicians: (u,v)=u*v; linear...

Thanks very much, PeterDonis. Hm, Indeed I appear to have read it too quickly, having been led astray by the summary by the journal at the beginning (which deceptively makes it sound as if there was a quantum aspect to the experiment), but I see from the quote by the author that “Since we...

I am not sure if this belongs in the biology section, but it appears more of a quantum physics question. Mike Wiest, Associate Professor of Neuroscience at Wellesley College in the US. In 2024 he published the results of an experiment on anaesthesia which purported to point to a role of...

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...