Fungrim entry: 00b82b

Symbol: Range —

\{a, a + 1, \ldots, b\}

— Integers between given endpoints

►Range(a, b) —

\{a, a + 1, \ldots, b\}

— Given

a \in \mathbb{Z}

and

b \in \mathbb{Z}

, represents

\left\{ n : n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, a \le n \le b \right\}

►Range(a, b) —

\{a, a + 1, \ldots, b\}

— Given

a \in \mathbb{Z}

and

b \in \mathbb{Z}

, is equivalent to Set(n, For(n, a, b)).

►Range(3, 3) —

\{3, 4, \ldots, 3\}

— Represents the singleton set {3}. Note: potentially confusing rendering.

►Range(3, 2) —

\{3, 4, \ldots, 2\}

— Represents the empty set. Note: potentially confusing rendering.

Definitions:

Fungrim symbol	Notation	Short description
`Range`	$\{a, a + 1, \ldots, b\}$	Integers between given endpoints
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("00b82b"),
    SymbolDefinition(Range, Range(a, b), "Integers between given endpoints"),
    CodeExample(Range(a, b), "Given", Element(a, ZZ), "and", Element(b, ZZ), ", represents", Set(n, ForElement(n, ZZ), LessEqual(a, n, b)), "."),
    CodeExample(Range(a, b), "Given", Element(a, ZZ), "and", Element(b, ZZ), ", is equivalent to", SourceForm(Set(n, For(n, a, b))), "."),
    CodeExample(Range(3, 3), "Represents the singleton set", Set(3), ".", " Note: potentially confusing rendering."),
    CodeExample(Range(3, 2), "Represents the empty set.", " Note: potentially confusing rendering."))

Topics using this entry

Numbers and infinities