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I am currently writing a master's dissertation. In this dissertation I have chosen to typographically separate logical argument, (Theorems, Proofs, and Definitions) from aids to understanding (Examples, Remarks and Asides).

Basically, sections that are intended to be rigorous is written in normal font, and sections that are intended to help the reader understand what is being written, but are not fundamental are written italicised.

The intention is simple: One who is familiar with the area is likely only checking definitions or theorems, and can focus on the normal text without hunting through a mountain of prose that they are already familiar with.

Someone who is new to the area, and who is not yet interested in the nitty-gritty details of a formal definition can focus on the italicised text, perhaps going back to the normal text later for something more concrete.

However my supervisor seems to think this is a bad idea, and has asked me to find precedents for this from well-known authors. Has anyone seen something like this before?

PS. When i say italicised, i actually mean only slanted. It's much easier to read than actually-italicised text. I could change the font to sans-serif for those sections.

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It is not a great idea, indeed. Using italics for what is achieved by hide tags in hypertext creates more strain to the eyes than convenience for the reader, IMHO. Print out and read 3 pages of italics and you'll see what I mean. However the idea to decide the issue based on the existence of "precedences from well-known authors" sounds even more ridiculous. You can just take any advertising brochure and bring it to your adviser showing the big text (FREE BOX OF CEREAL) and the fine print (with $1,000+ purchase). Anyway, voting to close as "not a real question". –  fedja Mar 22 '12 at 22:54
I searched Math Reviews for italicized/italicised in the review text, and came up with nothing like what you are suggesting. So, either no one has done it in a reviewed paper, or no reviewer has thought it worth mentioning. –  Gerry Myerson Mar 22 '12 at 22:54
If you want to separate those things (and you should), then you can do what everyone else does and use paragraphs. You can label examples, theorems, and definitions with subsection numbering, and preface paragraphs with "Aside: ..." or "Remark: ..." Older authors tended to use "NB: ..." for "nota bene." It should be obvious immediately when a paragraph is describing motivation or intuition, and when it is make a rigorous argument, so anyone reading just for one thing will know what to skip by reading the first line. Your goal, as author, is to make sure the separate ideas stay distinct. –  Zack Wolske Mar 22 '12 at 23:48
Long blocks of text in italics make my eyes hurt, and (if I correctly remember conversations with typography/DTP people from many years ago) are Thought Of As A Bad Thing. If you must change font, why not switch between roman/CM and sans serif? That said, I think Zack Wolske's suggestion is both the most obvious and the most sensible one, and I am voting to close as "off topic". –  Yemon Choi Mar 23 '12 at 1:25
Another preface that I rather like is "Proof sketch: ..." –  Qiaochu Yuan Mar 23 '12 at 9:28
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closed as off topic by fedja, Yemon Choi, Andres Caicedo, Chris Godsil, Mariano Suárez-Alvarez Mar 23 '12 at 4:22

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3 Answers

up vote 1 down vote accepted

If you really want to cite an example then you could say that Jantzen does this in the introduction to some of his chapters in "Lectures on Quantum Groups"

Rather than making a typographical distinction, why not just create a 'Remark' environment for chatty sections?

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I think that separating formal argument from aids to understanding is an excellent idea, and the usual way of doing it -- by an "end of proof" symbol and extra space before the next paragraph -- is not maximally clear. Someone skimming the text will not immediately know whether a random paragraph is part of a proof or part of a commentary or motivational remarks.

However, italics are hard on the eyes, so you need some other device. Perhaps ordinary font, but indented, and/or another font that is easier on the eyes, such as sans serif.

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Sans-serif is fine. I'm more interested in the citation that typographical advice though. –  user20886 Mar 23 '12 at 11:36
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I've seen books where some chatty stuff was put into margins, but you need really wide margins (or really short chats) for that. You certainly should have a "remark" environment, but I think the question is what it should do typographically. You might consider indentation, horizontal lines before and after, or a vertical line in the margin.

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two examples of books with marginal comments: Graham, Knuth, Patashnik's Concrete Mathematics and Goldrei's Classic Set Theory. –  m_t Mar 23 '12 at 12:22
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