Fungrim entry: c98bad

\operatorname{OpenDisk}\!\left(z, r\right) = \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z - t\right| \lt r \right\}

Assumptions:

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{R} \,\mathbin{\operatorname{and}}\, r \gt 0

TeX:

\operatorname{OpenDisk}\!\left(z, r\right) = \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z - t\right| \lt r \right\}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{R} \,\mathbin{\operatorname{and}}\, r \gt 0

Definitions:

Fungrim symbol	Notation	Short description
`SetBuilder`	$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$	Set comprehension
`CC`	$\mathbb{C}$	Complex numbers
`Abs`	$\left\|z\right\|$	Absolute value
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("c98bad"),
    Formula(Equal(OpenDisk(z, r), SetBuilder(t, t, And(Element(t, CC), Less(Abs(Sub(z, t)), r))))),
    Variables(z, r),
    Assumptions(And(Element(z, CC), Element(r, RR), Greater(r, 0))))

Topics using this entry

Complex plane