Difference between revisions of "Infinite"
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| − | ==Operations with Infinity== | + | =="Operations" with Infinity== |
| − | Some rules involving operations with infinity are as follows: | + | Some '''bad''' rules involving operations with infinity are as follows: |
| − | <math>1/{\infty} = 0</math> | + | * <math>1/{\infty} = 0</math> |
| − | <math>{\infty} + x = {\pm}{\infty}</math> | + | * <math>{\infty} + x = {\pm}{\infty}</math> |
| − | <math>{\infty}\cdot{x} = {\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 23:19, 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 
.
for a 
.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.
