uncountably love

# uncountably

## Definitions

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

## Etymologies

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.

• 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.

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

• 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).

• 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.

• 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 Weatherson, Brian 2009

• 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 MacFarlane, John 2009

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