0th

0th is the ordinal form of zero. In English, ordinal numbers indicate a position within an ordered sequence. For zero, the standard spoken form is zeroth, created by adding the ordinal suffix -th to zero. When written with digits, 0th is often used in technical or programming contexts, while zeroth is common in formal writing.

In mathematics and computer science, many constructs are zero-based, meaning indexing starts at zero. The element at index 0 is commonly called the zeroth element. In prose, zeroth is the preferred spelling, but in code or data identifiers, 0th may appear alongside a0 or similar notations.

Notable uses include the zeroth law of thermodynamics, which states that if two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other. The term is also present in fiction as the zeroth law of robotics, introduced by Isaac Asimov, which places a higher-priority rule above the original three laws.

Spelling and stylewise, zeroth is generally favored in mathematical and scientific writing, while 0th is common in software documentation, comments, and variable names that combine numerals with ordinal concepts. Both forms convey the same ordinal position, but zeroth is more widely accepted in formal contexts, and 0th appears more frequently in technical notation and programming.

See also: ordinal numbers, zero, zero-based indexing, indexing in programming.