Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • adv. Too many to be counted (either by reason of being infinite or for practical constraints).
  • adv. In an uncountable fashion.
  • adv. In a way that is incapable of being put into one-to-one correspondence with the natural numbers or any subset thereof.
  • adv. Used as a general intensifier of amounts and quantities; very; much

Etymologies

from Wiktionary, Creative Commons Attribution/Share-Alike License

uncountable +‎ -ly or un- +‎ countably

Examples

  • These sets are too big to be put into one-to-one correspondence with the natural numbers; they are called uncountably infinite.

    Skolem's Paradox

  • Thus, the one-to-one correspondence between the reals and the naturals fails, as there are simply too many reals—they are "uncountably" numerous—making real infinity somehow larger than natural infinity.

    Strange but True: Infinity Comes in Different Sizes | Impact Lab

  • For example, it certainly depends on whether your set of trials is countably infinite or uncountably infinite (in other words the cardinality of your set of trials).

    A Short Critique of Bradley Monton's Paper

  • * Eleanor Clift loses one of her uncountably many demerits in agitating for Howard Dean to HHS.

    Saturday Night « Gerry Canavan

  • Much to the consternation of marine life advocates and to the relief of the out-of-sight/out-of-mind crowd, most of the damage is uncountably ensconced beneath the surface of the Gulf.

    Vet's view: 10 biggest animal news stories of 2010

  • The questions raised by the uncountably infinite number of both unrealistic and implausible alternate viewpoints of diversity demand answers.

    Archive 2007-06-01

  • Or moving the other way, if we form a third language L³ by adding to L the quantifier Qx with the meaning “There are uncountably many elements x such that ¦”, then trivially L is reducible to L³, but the downward Loewenheim-Skolem theorem shows at once that L³ is not reducible to L.

    Model Theory

  • Or how might we have a little private time to tell just one of our sons of our affection for him without sharing the moment with uncountably many of his brothers?

    The Problem of the Many

  • Indeed, because cardinality is permutation-invariant, every cardinality quantifier is included, including “there are infinitely many”, “there are uncountably many”, and others that are not first-order definable.

    Logical Constants

  • How can a countable model satisfy the first-order sentence which “says that” there are uncountably many things?

    Skolem's Paradox

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