Meaning of a notation

Question

What is the meaning of the notation . I cannot search for such questions on google.

It can be used to denote a map from $I$ to $\mathbb{R}$, map and function are used interchangeably in many cases. Usually we call $\mathbb{R}$ the co-domain and $I$ the domain, the word "image" is reserved for the elements in the co-domain that are mapped to by the function given over the domain.i.e $f[I] \subset \mathbb{R}$ but not always $f[I] = \mathbb{R}$ — , Feb 23 '16 at 11:07

score 3 · Answer 1 · edited Feb 23 '16 at 11:05

3

It means that $f$ is a function from the set $I$ to the reals $\mathbb{R}$. Usually by $I$, one denotes an interval of $\mathbb{R}$.

edited Feb 23 '16 at 11:05

Patrick Stevens

36,135

answered Feb 23 '16 at 11:05

Onil90

2,703

score 1 · Answer 2 · answered Feb 23 '16 at 11:06

$f \colon I \to \mathbb R$ means that $f$ is a function with domain $I$ and range $\mathbb R$. So, for every $i \in I$ there is a unique $x \in \mathbb R$ (where $\mathbb R$ is the set of all real numbers) such that $(i,x) \in f$ (we also write $f(i) = x$ for this).

Meaning of a notation

2 Answers2