5

This is the question. The theorem is taken from someplace else. In my case, I want to use the asymmetric case of local lovasz lemma , and I am not sure if I should completely state it, or just refer the reader to (lemma 5.1.1 on pg ..).

If the answer is yes, the next question is where. Specifically, in the middle of the proof, it is strange to have all of a sudden another lemma. So I guess I should state it before the start of the lemma(should I write: I am about to use this lemma?).

Thanks.

6

Consider having an appendix/annex to the thesis where you state things that are essential to your argument and which your reader may want to see without looking elsewhere. For some things, perhaps in this case as well, a footnote citation of the lemma, including its name, might be enough since most people working in probability will know of it by name. Then, as a step in proving the current lemma/theorem, just refer to the footnote or appendix entry. The reader can take a detour if they feel it necessary.

But, you are correct not to make it hard to follow the flow of a proof.

A full statement of such a thing might be necessary if you were proving a variation or an extension of that thing. And in that case it might be necessary to work the statement and even, perhaps, a proof outline of the original into the text itself so it is clear how you are extending/modifying.

  • 2
    This advice seems oddly specific to theses. Such an appendix would be rather unusual in a paper. – Andrés E. Caicedo Feb 15 at 22:54
  • 1
    @AndrésE.Caicedo, yes, agreed in general, but there might be exceptions. See the tag on the question, however. – Buffy Feb 15 at 22:59
  • 1
    Yes, I noticed the tag. What still gives me pause, though, is that the same question will then reappear in a few months, when the person asking is now trying to write papers. In any case, this is one of those things that advisors may want to help novices with. – Andrés E. Caicedo Feb 15 at 23:16
11

For my taste, I'd "recall" the precise statement exactly when you need it, in the internals of your proof, as you seem to indicate. I myself have become ever fonder of a math writing style which does not require so much flipping back-and-forth to understand what's being said. (Especially the otherwise-precise quasi-Bourbaki of referring to things by some (necessarily artificial and meaningless) numbering scheme, rather than any sort of descriptive reference.)

In particular, for simply the statement (rather than proof) of a result, adding an appendix would make things harder to read for many people, and the people who already know the result would not gain much. Skipping over known things is easier than flipping back-and-forth.

That is, allowing your readers to read straight through seems to me the ideal. So, no, similarly, don't introduce all the notation at the beginning and then expect people to remember it. Sure, you could have an appendix for reference for notation, but it really should be explained when first used, ... in my opinion. That kind of thing.

  • I like this suggestion. I would add that it may be reasonable to "announce" one would be using the result. Saying something like "the following lemma makes use of [4] Theorem blah, whose statement we recall in due course". A reason is that a reader wanting to understand every detail may decide to take a look at [4] before reading the lemma rather than finding themselves having to pause in the middle if it. – Andrés E. Caicedo Feb 15 at 23:04
  • 3
    I think the Bourbakist reference style works fine with hyperlinks. To go even further, I wish HTML rather than PDF were the standard for mathematics papers, so that it would be possible to have mouseovers, collapsible text, and so forth. – Elizabeth Henning Feb 15 at 23:49
  • PDF provides a lot of abilities. I am not sure it is not possible. mouseovers do exists. – user2679290 Feb 16 at 15:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.