countable set in a sentence

One can identify a countable set of guesses for what the value of f is at any input, independent of G.
So \ aleph _ 1 cannot be written as the sum of a countable set of countable cardinal numbers, and is regular.
However, not every countable set is discrete, of which the rational numbers under the usual Euclidean metric are the canonical example.
I think the articles on countable set and bijection formalize this .-- T 08 : 25, 13 June 2009 ( UTC)
:: : : Beyond the observation that countable sets have zero Lebesgue measure, one can't say much relating measure and cardinality.

Banach spaces with a Schauder basis are necessarily separable, because the countable set of finite linear combinations with rational coefficients ( say ) is dense.
:The question's formulation seems to me to require improvement ( randomness from a countable set ), but it is clear what is meant.
This might be because it is difficult to draw or visualise a continuous function whose set of nondifferentiable points is something other than a countable set of points.
One observation about the game is that if X is a countable set, then either of the players can cause the final sum to avoid the set.
*PM : subsets of countable sets are countable, id = 7721 new !-- WP guess : subsets of countable sets are countable-- Status:

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