In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero. More generally, a binary relation R on a set...

Look up trichotomy in Wiktionary, the free dictionary. A trichotomy can refer to: Law of trichotomy, a mathematical law that every real number is either...

single operation, in accordance with the mathematical law of trichotomy. It can be implemented in terms of a function (such as strcmp in C), a method (such...

A trichotomy is a three-way classificatory division. Some philosophers pursued trichotomies. Important trichotomies discussed by Aquinas include the causal...

cardinality of A is said to be strictly smaller than the cardinality of B. This is denoted |A| < |B|. If the axiom of choice holds, then the law of trichotomy holds...

}}x<0,\\0&{\text{if }}x=0,\\1&{\text{if }}x>0.\end{cases}}} The law of trichotomy states that every real number must be positive, negative or zero....

For more detail, see § Cardinality of the continuum below. If the axiom of choice holds, the law of trichotomy holds for cardinality. Thus we can make...

important preliminary theorems, for example, a generalized form of law of trichotomy, were derived within what Frege understood to be pure logic. This...

x\cong 0} and indeed at most one of the three can hold at once. But the stronger, logically positive law of trichotomy disjunction does not hold in general...

exactly one of x < y, x = y, x > y, holds (law of trichotomy). This means that < is a linear order (except that < is a proper class). For sets of numbers...