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transfinite Definition

trans·fi·nite (-fī′nīt)

adjective

  1. extending beyond or surpassing the finite
  2. Math. designating or of a cardinal or ordinal number that is larger than any positive integer

transfinite Usage Examples

Modifies a noun

  • induction: His proof of the well ordering property used the axiom of choice to construct sets by transfinite induction.
  • number: Cantor held that these transfinite numbers had an actual existence, drawing on his early religious training to justify the assertion.
  • ordinal: Our ability to think about transfinite ordinals is one of the things to be explained.
  • cardinal: Recall that " addition " for transfinite cardinals is defined in terms of set union.
  • mathematics: When the imaginary transfinite mathematics of the actual infinite is translated into real finite terms, the results are nonsensical.
  • case: Finally, we extend the theory of needed reduction from the finite to the transfinite case.