Transfinite in A Sentence

    1

    Cantor held that these transfinite numbers had an actual existence, drawing on his early religious training to justify the assertion.

    2

    Finally, we extend the theory of needed reduction from the finite to the transfinite case.

    3

    His proof of the well ordering property used the axiom of choice to construct sets by transfinite induction.

    4

    Our ability to think about transfinite ordinals is one of the things to be explained.

    5

    Recall that " addition " for transfinite cardinals is defined in terms of set union.

    6

    When the imaginary transfinite mathematics of the actual infinite is translated into real finite terms, the results are nonsensical.