# Fungrim entry: 978576

Symbol: ForElement $\ldots$ Generator for all the elements of a set
ForElement(x, S) declares the variable x just like For(x) and additionally tells the parent operator that $x$ is to range over the elements of the set $S$. Examples: Set(Mul(2, n), ForElement(n, ZZ)) becomes $\left\{ 2 n : n \in \mathbb{Z} \right\}$. Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0)))) becomes $\sum_{n \in \mathbb{Z} \setminus \left\{0\right\}} \frac{1}{{n}^{2}}$.
Definitions:
Fungrim symbol Notation Short description
ZZ$\mathbb{Z}$ Integers
Sum$\sum_{n} f(n)$ Sum
Pow${a}^{b}$ Power
Source code for this entry:
Entry(ID("978576"),
SymbolDefinition(ForElement, Ellipsis, "Generator for all the elements of a set"),
Description(SourceForm(ForElement(x, S)), "declares the variable", SourceForm(x), "just like", SourceForm(For(x)), "and additionally tells the parent operator", "that", x, "is to range over the elements of the set", S, ". ", "Examples: ", SourceForm(Set(Mul(2, n), ForElement(n, ZZ))), "becomes", Set(Mul(2, n), ForElement(n, ZZ)), ". ", SourceForm(Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0))))), "becomes", Sum(Div(1, Pow(n, 2)), ForElement(n, SetMinus(ZZ, Set(0)))), ". "))

## Topics using this entry

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