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Countable Axiom Of Choice Bijection Prime Finite Uncountable Real Number Empty Set Interval Egyptian Fraction Dedekind Infinite Axiom Of Countable Choice
| 1 | Interval |
| 1 | Real Number |
| 1 | Empty Set |
| 1 | Finite |
| 1 | Axiom Of Choice |
| 1 | Countable |
| 1 | Uncountable |
| 1 | Bijection |
| 1 | Prime |
| 2 | Egyptian Fraction |
| 4 | Dedekind Infinite |
| 4 | Axiom Of Countable Choice |
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Infinite
A set 
is infinite if it is not finite; that is, there is no
for which there is a bijection
between 
and 
.
Assuming the Axiom of Choice (or the Axiom of Countable Choice), this definition of infinite sets is equivalent to that of Dedekind-infinite sets.
Some examples of finite sets:
- The empty set:
.
-
-
Some examples of infinite sets:
-
.
- The primes:
.
- The rational numbers:
.
- An interval
of the reals:
.
The first three examples are countable, but the last is uncountable.