Difference between revisions of "Infinite"

Latest revision as of 22:19, 16 August 2013

A set $S$ is said to be infinite if there is a surjection $f:S\to\mathbb{Z}$ . If this is not the case, $S$ 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 $\{1, 2, \ldots, n\}$ for a positive integer $n$ .

A sum works the same way. Certain sums equate to infinity, such as

$\sum_{i = 3}^{\infty}{(2i - 1)}$

This article is a stub. Help us out by expanding it.

Some bad rules involving operations with infinity are as follows:

None of these are true because $\infty$ is not a real number which you can write equations involving.

@@ Line 6: / Line 6: @@
 * A set is infinite if it can be put into [[bijection]] with one of its proper [[subset]]s.
 * A set is infinite if it is not empty and cannot be put into bijection with any set of the form <math>\{1, 2, \ldots, n\}</math> for a [[positive integer]] <math>n</math>.
+==Applications to Infinity with Sums==
+A sum works the same way. Certain sums equate to infinity, such as
+<math>\sum_{i = 3}^{\infty}{(2i - 1)}</math>
 {{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.