Difference between revisions of "Infinite"
m (→Equivalent formulations) |
(→Operations with Infinity) |
||
(One intermediate revision by one other user not shown) | |||
Line 14: | Line 14: | ||
{{stub}} | {{stub}} | ||
+ | |||
+ | |||
+ | =="Operations" with Infinity== | ||
+ | |||
+ | Some '''bad''' rules involving operations with infinity are as follows: | ||
+ | |||
+ | * <math>1/{\infty} = 0</math> | ||
+ | |||
+ | * <math>{\infty} + x = {\pm}{\infty}</math> | ||
+ | |||
+ | * <math>{\infty}\cdot{x} = {\infty}</math> | ||
+ | |||
+ | None of these are true because <math>\infty</math> is not a real number which you can write equations involving. |
Latest revision as of 22:19, 16 August 2013
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.