One can identify a countable set of guesses for what the value of f is at any input, independent of G.
22.
So \ aleph _ 1 cannot be written as the sum of a countable set of countable cardinal numbers, and is regular.
23.
However, not every countable set is discrete, of which the rational numbers under the usual Euclidean metric are the canonical example.
24.
I think the articles on countable set and bijection formalize this .-- T 08 : 25, 13 June 2009 ( UTC)
25.
:: : : Beyond the observation that countable sets have zero Lebesgue measure, one can't say much relating measure and cardinality.
26.
Banach spaces with a Schauder basis are necessarily separable, because the countable set of finite linear combinations with rational coefficients ( say ) is dense.
27.
:The question's formulation seems to me to require improvement ( randomness from a countable set ), but it is clear what is meant.
28.
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.
29.
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.
30.
*PM : subsets of countable sets are countable, id = 7721 new !-- WP guess : subsets of countable sets are countable-- Status:
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