When and where to italicize a term in text?

Question

Assume that the following text are excerpts from a book ...

Book: Fun with Math

Chapter 1: We will learn about lots of numbers like integers, real, even numbers and odd numbers.

Chapter 2: There are two kinds of numbers: even numbers and odd numbers.

Chapter 3: An even number is a number which is divisible into two equal integers.

Of the three locations that even number appears in, where is it recommended to italicize it? Is it when it is mentioned (chapter 1), described (chapter 2) or when defined (chapter 3)? Or is it preferred to italicize it in multiple or all appearances?

A more general question is: is a term italicized when it first appears or when it is actually defined? The locations of these two might be far apart in the text.

I think that in formal math texts, you italicize it within or right before the definition. Another possibility is that you can informally present it beforehand, such as "an even number divides evenly" (in which case you italicize it) and later on, give a formal definition "an even number is a positive integer x such that 2 divides x" (no italics again). — Bogdan Lataianu, Aug 30 '11 at 07:37
This question is more about style, rather than English itself. Voting to migrate to the Writers SE. :) — Alenanno, Aug 30 '11 at 15:50
possible duplicate of Should this word be in quotes or in italic? — apaderno, Aug 31 '11 at 11:56

score 1 · Answer 1 · edited Jun 15 '20 at 07:40

Wikipedia has some good advice on this topic. A summary of the bits that seem like they might be relevant here:

Mentioning a word as an example of a word rather than for its semantic content (see use–mention distinction): "The word the is an article".

Using a letter or number mentioned as itself.

Introducing or defining terms, especially technical terms or those used in an unusual or different way: "An even number is one that is a multiple of 2."

I think there's some room for interpretation, but here's my take as it relates to your specific questions: The Chapter 3 part would certainly take italics, because there you're defining terms. I'd use it for Chapter 2 as well, especially if that's the first mention of the term. I wouldn't use it for Chapter 1, because there you're not defining the term, and the phrase has a referent—actual even numbers.

The wording in Wikipedia regarding your final question is ambiguous, I think: introducing could mean "writing for the first time", or it could mean "quickly or informally defining." I'm inclined to go with the latter, and so I wouldn't use italics for the first use of a phrase if I didn't define the phrase at that point.

When and where to italicize a term in text?

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