Category:Definitions/Infinity
This category contains definitions related to Infinity.
Related results can be found in Category:Infinity.
Informally, the term infinity is used to mean some infinite number, but this concept falls very far short of a usable definition.
The symbol $\infty$ (supposedly invented by John Wallis) is often used in this context to mean an infinite number.
However, outside of its formal use in the definition of limits its use is strongly discouraged until you know what you're talking about.
It is defined as having the following properties:
| \(\ds \forall n \in \Z: \, \) | \(\ds n\) | \(<\) | \(\ds \infty\) | ||||||||||||
| \(\ds \forall n \in \Z: \, \) | \(\ds n + \infty\) | \(=\) | \(\ds \infty\) | ||||||||||||
| \(\ds \forall n \in \Z: \, \) | \(\ds n \times \infty\) | \(=\) | \(\ds \infty\) | ||||||||||||
| \(\ds \infty^2\) | \(=\) | \(\ds \infty\) |
Similarly, the quantity written as $-\infty$ is defined as having the following properties:
| \(\ds \forall n \in \Z: \, \) | \(\ds -\infty\) | \(<\) | \(\ds n\) | ||||||||||||
| \(\ds \forall n \in \Z: \, \) | \(\ds -\infty + n\) | \(=\) | \(\ds -\infty\) | ||||||||||||
| \(\ds \forall n \in \Z: \, \) | \(\ds -\infty \times n\) | \(=\) | \(\ds -\infty\) | ||||||||||||
| \(\ds \paren {-\infty}^2\) | \(=\) | \(\ds -\infty\) |
The latter result seems wrong when you think of the rule that a negative number squared equals a positive number, but remember that infinity is not exactly a number as such.
Subcategories
This category has the following 3 subcategories, out of 3 total.
A
C
P
Pages in category "Definitions/Infinity"
The following 10 pages are in this category, out of 10 total.