587 views
1 votes
1 votes
I wanted an example of a set which is infinite and countable. Is hair on human head an example of countable set being infinite?

1 Answer

1 votes
1 votes
Countability, when it comes to infinite sets, should not be taken as its normal meaning.

A set is said to be countable if there exists a bijection between its elements and the set of natural numbers - that's all. No matter how unintuitive it might feel, if it meets this condition, the set is countable.

So hair on head is a countable set because there exists such a bijection. Same with set of natural numbers, set of positive rational numbers etc.

Related questions

1 votes
1 votes
3 answers
1
0 votes
0 votes
0 answers
2
ankitgupta.1729 asked Dec 3, 2017
213 views
How to know whether a enumeration method exist or not for a given set to prove it countable?? For example how to know that set of irrational numbers is countable or not.....