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.
- 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
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