countable set
a set 
is said to be countably infinite (or just countable) iff it has equal cardinality with the broken link: blk:def-natural-set-inf 
. a set is said to be at most countable iff it is either countable or finite. we say that a set is uncountable if it is infinite but not countable.
[cite:;taken from @tao_analysis_1 definition 8.1.1]
the same definition can be found in [cite:;in @analysis_cummings_2019 chapter 2 cardinality; definition 2.10]. is said to be countably infinite (or just countable) iff it has equal cardinality with the broken link: blk:def-natural-set-inf . a set is said to be at most countable iff it is either countable or finite. we say that a set is uncountable if it is infinite but not countable.[cite:;taken from @tao_analysis_1 definition 8.1.1]