Infinite
A set is said to be infinite if there is a surjection . If this is not the case, is said to be finite.
In simplified language, a set is infinite if it doesn't end, i.e. you can always find another element that you haven't examined yet.
Equivalent formulations
- A set is infinite if it can be put into bijection with one of its proper subsets.
- A set is infinite if it is not empty and cannot be put into bijection with any set of the form for a positive integer .
Applications to Infinity with Sums
A sum works the same way. Certain sums equate to infinity, such as
This article is a stub. Help us out by expanding it.
"Operations" with Infinity
Some bad rules involving operations with infinity are as follows:
None of these are true because is not a real number which you can write equations involving.