0th

0th or zeroth is a conceptually fallacious attempt to create an ordinal insertion (preceding the first element) for the cardinal number zero sometimes used under zero-based numbering, and can refer to:

• 0th grade, another name for kindergarten
• 0th dimension
• 0th planet, a name for Vulcan (hypothetical planet)
• 0th United States Congress, also called the Congress of the Confederation
• January 0 or January 0th, an alternate name for December 31
• The zeroth law of thermodynamics
• Zeroth-order logic
• The Zeroth Law, an addition to Isaac Asimov's Three Laws of Robotics
• Zeroth order approximation; see Orders of approximation
• Zeroth, the fastest demo or highest score on a level or episode in N (video game)
• Zeroth, deep learning software for mobile devices

Distinguish from

• Oth or OTH (with a letter O)

The problem arises in the attempt to move from the ordinal numbering system to the cardinal numbering system. In cardinal numbering, elements of a set are assigned values starting at the first element; the first element may be element number one or element number zero. The fallacy arises when the user attempts to create an ordinal numbering of a value by using a superscript on the cardinal number. Since there is nothing preceding the first element, whether its value is zero or one, the result is a fallacious first element preceding the first element, invalidating the constraints of the cardinal numbering system.