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Fungrim entry: c98bad

OpenDisk⁡ ⁣(z,r)={t:t∈C and⁡ ∣z−t∣<r}\operatorname{OpenDisk}\!\left(z, r\right) = \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z - t\right| < r \right\}
Assumptions:z∈C  and⁡  r∈R  and⁡  r>0z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; r \in \mathbb{R} \;\mathbin{\operatorname{and}}\; r > 0
TeX:
\operatorname{OpenDisk}\!\left(z, r\right) = \left\{ t : t \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z - t\right| < r \right\}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; r \in \mathbb{R} \;\mathbin{\operatorname{and}}\; r > 0
Definitions:
Fungrim symbol Notation Short description
CCC\mathbb{C} Complex numbers
Abs∣z∣\left|z\right| Absolute value
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("c98bad"),
    Formula(Equal(OpenDisk(z, r), Set(t, ForElement(t, CC), Less(Abs(Sub(z, t)), r)))),
    Variables(z, r),
    Assumptions(And(Element(z, CC), Element(r, RR), Greater(r, 0))))

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

2021-03-15 19:12:00.328586 UTC