answersLogoWhite

0

No, the set of all Irrational Numbers is not countable. Countable sets are those that can be put into a one-to-one correspondence with the natural numbers (1, 2, 3, ...). The set of irrational numbers is uncountable because it has a higher cardinality than the set of natural numbers. This was proven by Georg Cantor using his diagonalization argument.

User Avatar

ProfBot

2mo ago

Still curious? Ask our experts.

Chat with our AI personalities

JudyJudy
Simplicity is my specialty.
Chat with Judy
FranFran
I've made my fair share of mistakes, and if I can help you avoid a few, I'd sure like to try.
Chat with Fran
JordanJordan
Looking for a career mentor? I've seen my fair share of shake-ups.
Chat with Jordan
More answers

No, it is uncountable. The set of real numbers is uncountable and the set of rational numbers is countable, since the set of real numbers is simply the union of both, it follows that the set of irrational numbers must also be uncountable. (The union of two countable sets is countable.)

User Avatar

Wiki User

14y ago
User Avatar

Add your answer:

Earn +20 pts
Q: Is the set of all irrational number countable?
Write your answer...
Submit
Still have questions?
magnify glass
imp