The real numbers/Infobox
From Maths
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 innerproduct 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 xy\Vert\eq \vert xy\vert[/ilmath]  Absolute value  Euclidean metric on [ilmath]\mathbb{R}^1[/ilmath] 
topology  topology induced by the metric [ilmath]d[/ilmath] 
Standard measuretheoretic structures  
measurable space  Borel [ilmath]\sigma[/ilmath]algebra of [ilmath]\mathbb{R} [/ilmath]^{[Note 1]} 

Lebesguemeasurable sets of [ilmath]\mathbb{R} [/ilmath]

The real line discusses [ilmath]\mathbb{R} [/ilmath] as a set.
Notes
 ↑ This is just the Borel sigmaalgebra on the real line (with its usual topology)