ordering

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Figure 1: Illustration of an axiom of order.

ordering

logic and mathematics

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set theory
Cardinality and transfinite numbers
To compare cardinal numbers, an ordering relation (symbolized by <) may be introduced by means of the definition if A is equivalent to a subset of B and B is equivalent to no subset of A. Clearly, this relation is irreflexive and transitive:
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To compare cardinal numbers, an ordering relation (symbolized by <) may be introduced by means of the definition if A is equivalent to a subset of B and B is equivalent to no subset of A. Clearly, this relation is irreflexive and transitive:
Read More