# Fungrim entry: c8a5f0

Symbol: LeftLimit $\lim_{x \to {a}^{-}} f(x)$ Limiting value, from the left
This operator can be called with three or four arguments.
LeftLimit(f(x), For(x, a)), rendered as $\lim_{x \to {a}^{-}} f(x)$, is equivalent to Limit(f(x), For(x, a), Element(x, OpenInterval(Neg(Infinity), a))).
LeftLimit(f(x), For(x, a), P(x)), rendered as $\lim_{x \to {a}^{-},\,P(x)} f(x)$, is equivalent to Limit(f(x), For(x, a), And(Element(x, OpenInterval(Neg(Infinity), a)), P(x))).
The expression For(x, a) declares x as a locally bound variable within the scope of the arguments to this operator.
Definitions:
Fungrim symbol Notation Short description
LeftLimit$\lim_{x \to {a}^{-}} f(x)$ Limiting value, from the left
Limit$\lim_{x \to a} f(x)$ Limiting value
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("c8a5f0"),
SymbolDefinition(LeftLimit, LeftLimit(f(x), For(x, a)), "Limiting value, from the left"),
Description("This operator can be called with three or four arguments."),
Description(SourceForm(LeftLimit(f(x), For(x, a))), ", rendered as", LeftLimit(f(x), For(x, a)), ", is equivalent to", SourceForm(Limit(f(x), For(x, a), Element(x, OpenInterval(Neg(Infinity), a)))), "."),
Description(SourceForm(LeftLimit(f(x), For(x, a), P(x))), ", rendered as", LeftLimit(f(x), For(x, a), P(x)), ", is equivalent to", SourceForm(Limit(f(x), For(x, a), And(Element(x, OpenInterval(Neg(Infinity), a)), P(x)))), "."),
Description("The expression", SourceForm(For(x, a)), "declares", SourceForm(x), "as a locally bound variable within the scope of the arguments to this operator."))

## 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