0
A countable set is an infinite set that can be put into a one-to one correspondence with the counting numbers. In other words, it is possible to arrange all of the elements of the set in a sequence with a first element, a second element, and so on.
Georg Cantor proved that the rational numbers are countable, but the real numbers are not.
One proof (not Cantor's) that the rationals are countable: Choose any rational number, write it out in its simplest form. Whatever number you wrote is represented by a finitely long string of either the numerals or the division slash (possibly preceded the negative sign). If you consider a base-eleven number system with the division slash as the eleventh numeral, then whatever rational number you just wrote out corresponds directly and unambiguously to one specific integer. Since there exists a mapping scheme that assigns any arbitrary rational number to a specific integer, the rational numbers are countable.
Still curious? Ask our experts.
Chat with our AI personalities
Judy
Fran
RafaAdd your answer:
Earn +20 pts
What is the Difference between a finite set and countable set?
all finite set is countable.but,countable can be finite or infinite
What definition proves that the set of all odd natural numbers is a countable set?
It is NOT a 'countable set'. It is an infinite set. 1, 3, 5, 7, 9, 11, ... you can count to infinity and keep going.
What are the different types a of set?
A null set, a finite set, a countable infinite set and an uncountably infinite set.
Can infinity be an element of a set?
Yes.The set of {Aleph-null, Aleph-one, ...}, which is the set of the different infinities, has infinity as an element.Aleph-null is the countable infinity.
What is the difference between classical set theory and fuzzy set theory?
Classical theory is a reference to established theory. Fuzzy set theory is a reference to theories that are not widely accepted.
