The real numbers/Infobox

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]
- other:	Lebesgue-measurable sets of [ilmath]\mathbb{R} [/ilmath] contains the Borel [ilmath]\sigma[/ilmath]-algebra

The real line discusses [ilmath]\mathbb{R} [/ilmath] as a set.