Real Analysis : Countable Sets and Antichains
Answer the following by establishing 1-1(one to one) correspondence with a set of known cardinality:
1 - Is the set of all functions from{0,1} to N countable or noncountable?
2 - Is the set of all functions from N to {0,1} countable or noncountable?
3 - Given a set B ,a subset A of P(B) is called an antichain if no element of A is a subset of any other element of A. Does P(N) contain an uncountable antichain?
https://brainmass.com/math/real-analysis/real-analysis-countable-sets-and-antichains-26064
Solution Preview
1. countable
For each of f from {0,1} to N, we consider two cases. If f(0)=f(1), then each such f is corresponding to one element f(0) in N. So it is countable. If f(0)<>f(1), then each such f is corresponding ...
Solution Summary
Countability of sets is analyzed.
$2.19