answersLogoWhite

0

Infinity but (are you ready for this?) the smallest of infinities, which is Aleph-zero.

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

LaoLao
The path is yours to walk; I am only here to hold up a mirror.
Chat with Lao
RossRoss
Every question is just a happy little opportunity.
Chat with Ross
DevinDevin
I've poured enough drinks to know that people don't always want advice—they just want to talk.
Chat with Devin

Add your answer:

Earn +20 pts
Q: What is the cardinality of the set of rational numbers?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Other Math

Is the set of irrational numbers countably infinite?

No. The set of irrational numbers has the same cardinality as the set of real numbers, and so is uncountable.The set of rational numbers is countably infinite.


What is infinity squared?

Infinity squared is infinity. But there's more to it.Mathematicians describe different kinds of infinities:The cardinality(number) of natural numbers is called Aleph0 () . This is infinite, and it has some peculiar properties:The cardinality of even numbers is also Aleph0.As is the cardinality of odd numbers.As is the cardinality of rational numbers (which you could view as infinity squared, but it still gives you infinity.The cardinality of countable ordinal numbers is called Aleph1 ().The cardinality of the real numbers is two to the exponent of Aleph0 ( ). The continuum hypothesis says this is equal to Aleph1.Basically, if you square an infinite set from a given cardinality, the cardinality stays the same (meaning Aleph0 squared is still Aleph0, etc.)If your mind just burst(cause mine did! 0_o), do not worry. This is a common reaction to set theory.See the related link for more on Aleph numbers, which are how mathematicians view infinity.


Derived Set of a set of Rational Numbers?

The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.


What is the sum of the rational numbers?

The sum of any finite set of rational numbers is a rational number.


What is a set of rational and irrational numbers?

It is the set of Real numbers.