Difference between revisions of "The real numbers/Infobox"
From Maths
(Moved infobox to separate page. Made box a little wider to support title.) |
m (Alec moved page Real line/Infobox to The real numbers/Infobox without leaving a redirect: Moving to "the real numbers" which was a redirect page here) |
(No difference)
| |
Latest revision as of 21:31, 26 February 2017
| The real numbers | |
[ilmath]\mathbb{R} [/ilmath]
| |
| Algebraic structure | |
|---|---|
TODO: Todo - is a field
| |
| Standard topological structures | |
| Main page: The real line | |
| inner product | [ilmath]\langle a,b\rangle:\eq a*b[/ilmath] - Euclidean inner-product on [ilmath]\mathbb{R}^1[/ilmath] |
| norm | [ilmath]\Vert x\Vert:\eq\sqrt{\langle x,x\rangle}\eq\vert x\vert[/ilmath] - Euclidean norm on [ilmath]\mathbb{R}^1[/ilmath] |
| metric | [ilmath]d(x,y):\eq\Vert x-y\Vert\eq \vert x-y\vert[/ilmath] - Absolute value - Euclidean metric on [ilmath]\mathbb{R}^1[/ilmath] |
| topology | topology induced by the metric [ilmath]d[/ilmath] |
| Standard measure-theoretic structures | |
| measurable space | Borel [ilmath]\sigma[/ilmath]-algebra of [ilmath]\mathbb{R} [/ilmath][Note 1] |
|
Lebesgue-measurable sets of [ilmath]\mathbb{R} [/ilmath]
|
The real line discusses [ilmath]\mathbb{R} [/ilmath] as a set.
Notes
- ↑ This is just the Borel sigma-algebra on the real line (with its usual topology)
