Difference between revisions of "The real numbers/Infobox"

	The real numbers
	R
Algebraic structure
	TODO: Todo - is a field
Standard topological structures
	Main page: The real line
inner product	⟨a,b⟩:=a∗b; - Euclidean inner-product on R1
norm	∥x∥:=√⟨x,x⟩=\|x\|; - Euclidean norm on R1
metric	d(x,y):=∥x−y∥=\|x−y\|; - Absolute value; - Euclidean metric on R1
topology	topology induced by the metric d
Standard measure-theoretic structures
measurable space	Borel σ-algebra of R
- other:	Lebesgue-measurable sets of R contains the Borel σ-algebra;

Latest revision as of 21:31, 26 February 2017

The real line discusses $\mathbb{R}$ as a set.

Revision as of 21:28, 26 February 2017 (view source) Alec (Talk \| contribs) (Moved infobox to separate page. Made box a little wider to support title.)	Latest revision as of 21:31, 26 February 2017 (view source) Alec (Talk \| contribs) 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)

Algebraic structure
The real numbers
$\mathbb{R}$
TODO: Todo - is a field
Standard topological structures
Main page: The real line
inner product	$\langle a,b\rangle:\eq a*b$ - Euclidean inner-product on $\mathbb{R}^1$
norm	$\Vert x\Vert:\eq\sqrt{\langle x,x\rangle}\eq\vert x\vert$ - Euclidean norm on $\mathbb{R}^1$
metric	$d(x,y):\eq\Vert x-y\Vert\eq \vert x-y\vert$ - Absolute value - Euclidean metric on $\mathbb{R}^1$
topology	topology induced by the metric $d$
Standard measure-theoretic structures
measurable space	Borel $\sigma$ -algebra of $\mathbb{R}$ ^{[Note 1]}
- other:	Lebesgue-measurable sets of $\mathbb{R}$ contains the Borel $\sigma$ -algebra