Show that R has 2 1 uncountable dense subsetsSolutionSince i

Show that R has 2^{ ₁} uncountable dense subsets

Since irrationals are uncountable, so their cardinality is 2^N. Set of rationals Q is countable and dense subset of R, so kQ is countable and dense subset of R, where k is irrational number. Therefore number of kQ is uncountable, so cardinality of kQ is 2^N

$Show that R has 2^{ 1} uncountable dense subsetsSolutionSince irrationals are uncountable, so their cardinality is 2^N. Set of rationals Q is countable and dens$

Show that R has 2 1 uncountable dense subsetsSolutionSince i

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