Convention is a statement or rule of practice which by common consent, express or implied, is employed in the solution of a given class of problems or guides behavior in a certain kind of situation. A convention, as distinct from an axiom, may be said to exist when it is known that an alternative, equally logical rule or procedure is available but is not used because of considerations of habit, cost, time, or convenience. Thus, the convention of omitting the characteristic in the construction of logarithm tables increases their convenience and saves time and cost in their compilation and publication.

The adoption of a particular convention may even be a historical accident, but once adopted, a convention acquires value as a means of communication and cooperation. Thus, many other signs were employed for arithmetic operations when “+” and “-” were introduced by Widmann in 1489 and these were not commonly accepted until the 17th century, but they became a part of the mathematician’s stock-in-trade because they conveyed meaning without elaborate explanations or translations. An axiom and a convention may be indistinguishable, thus the use of straight-line depreciation in many cases, long regarded as a convention, has tended to take on the character of an axiom as it becomes increasingly clear that alternative methods are neither more logical, rigorous, nor accurate, and as its propriety and utility are less often challenged.

Ultimately, the choice of axioms must be regarded as conventional. A particular set of axioms may be regarded as a set of conventions in that alternative systems can be devised in which what are now theorems are used as the starting points, and what are now axioms become theorems.

Conventionality does not, however, impair the analytical usefulness of axioms. It merely implies that if an unconventional system is demonstrated to possess greater analytical power, fecundity, or simplicity, the only obstacle to its adoption is the accumulated habits of the professional community.