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Fungrim entry: c98bad

OpenDisk ⁣(z,r)={t:tCandzt<r}\operatorname{OpenDisk}\!\left(z, r\right) = \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z - t\right| \lt r \right\}
Assumptions:zCandrRandr>0z \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{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
RRR\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

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC