Ties avoid bad line breaks

Use non-breaking spaces, also called ties, to prevent the computer breaking lines in bad places: the concept of "badness" is subjective and so hard to code definite rules; apply the principles with artist taste. I quote here, virtually verbatim from Donald Knuth, a list of examples to show the range of considerations. These apply to all typesetting, not just LaTeX.

Use ties in cross-reference: Theorem~A; Algorithm~B; Chapter~3; Table~4; Programs E and~F. No tie appears after "Programs" in the last example since it would be quite all right to have "E and F" at the beginning of a line.
Use ties between a person's forenames and between multiple surnames: Dr.~I.~J. Matrix; Luis~I. Trabb~Pardo; Peter van~Emde~Boas. Notice that it is better to hyphenate a name rather than to break it between words.
Use ties for symbols in apposition with nouns: base~b; dimension~d; function~f(x); string~s of length~l. But compare the last example with "string~s of length l~or more".
Use ties for symbols in series: 1,~2, or~3; a,~b, and~c; 1,~2,...,~n
Use ties for symbols as tightly-bound objects of prepositions: of~x; from 0 to~1; increase z by~1; in common with~m. This rule does not apply to compound objects: for example, consider "of u~and~v".
Use ties to avoid breaking up mathematical phrases that are rendered in words: equals~n; less than~e; mod~2; modulo~p^e; (given~X); when x~grows; if t~is... Compare "is~15" with "is 15~times the height"; and compare "for all large~n" with "for all n~greater than~n₀.
Use ties when enumerating cases: "(b)~Show that f(x) is (1)~continuous; (2)~bounded.

I took this list of examples from pp. 89--90 of Digital typography by D. E. Knuth, CSLI Publications, 1999; originally written with M. F. Plass and appearing in Software---Practice and Experience 11 (1981), 1119--1184.

LaTeX: from quick and dirty to style and finesse

by Prof Tony Roberts

Ties avoid bad line breaks

	LaTeX: from quick and dirty to style and finesse by Prof Tony Roberts


LaTeX Intro Home Quick start Environments Cross referencing More mathematics Figures to seminars Write right Art of ties Use colour Home pages Tony Roberts Maths and Comp Sciences USQ	Ties avoid bad line breaks Use non-breaking spaces, also called ties, to prevent the computer breaking lines in bad places: the concept of "badness" is subjective and so hard to code definite rules; apply the principles with artist taste. I quote here, virtually verbatim from Donald Knuth, a list of examples to show the range of considerations. These apply to all typesetting, not just LaTeX. Use ties in cross-reference: Theorem~A; Algorithm~B; Chapter~3; Table~4; Programs E and~F. No tie appears after "Programs" in the last example since it would be quite all right to have "E and F" at the beginning of a line. Use ties between a person's forenames and between multiple surnames: Dr.~I.~J. Matrix; Luis~I. Trabb~Pardo; Peter van~Emde~Boas. Notice that it is better to hyphenate a name rather than to break it between words. Use ties for symbols in apposition with nouns: base~b; dimension~d; function~f(x); string~s of length~l. But compare the last example with "string~s of length l~or more". Use ties for symbols in series: 1,~2, or~3; a,~b, and~c; 1,~2,...,~n Use ties for symbols as tightly-bound objects of prepositions: of~x; from 0 to~1; increase z by~1; in common with~m. This rule does not apply to compound objects: for example, consider "of u~and~v". Use ties to avoid breaking up mathematical phrases that are rendered in words: equals~n; less than~e; mod~2; modulo~p^e; (given~X); when x~grows; if t~is... Compare "is~15" with "is 15~times the height"; and compare "for all large~n" with "for all n~greater than~n₀. Use ties when enumerating cases: "(b)~Show that f(x) is (1)~continuous; (2)~bounded. I took this list of examples from pp. 89--90 of Digital typography by D. E. Knuth, CSLI Publications, 1999; originally written with M. F. Plass and appearing in Software---Practice and Experience 11 (1981), 1119--1184. Copyright Tony Roberts, Dept Mathematics and Computing, USQ, Toowoomba, Australia; prepared January 16, 2008, from `site.tex` CRICOS: QLD 00244B \| NSW 02225M \| VIC 02387D