2
$\begingroup$

What does this mean: ($f$ a function, $I$ an interval and $R$ the real numbers)

$f \in C(I,R)$

Does it mean $f$ is an element of the collection of continuous functions with domain $I$ and range $R$ ? (literal translation so the terms might be off)

Also, what would this mean:

$f \in C^\infty(I,R)$ ?

  • 0
    Technically, $f$ is an element of the collection of continuous functions with domain $I$ and *codomain* $R$. (There is no requirement that $f$ be onto.) A shorter way to read this would be "$f$ is a continuous function from $I$ to $R$".2011-01-11

1 Answers 1

7
  1. $C(I,R)$ is the space of continuous functions from $I$ to $R$.

  2. $C^{\infty}(I,R)$ is the space of smooth functions from $I$ to $R$. That is, $f$ has derivatives of all orders.