Excel in math, science, and engineering

New user? Sign up

Existing user? Sign in

Find an example of a function that is nowhere continuous but whose absolute value is everywhere continuous.

Note by Hobart Pao 1 year, 9 months ago

Sort by:

\[f : \mathbb{R} \to \mathbb{R}, \forall x f(x) = \begin{cases} 1 & \text{if $x \in \mathbb{Q}$} \\ -1 & \text{if $x \not\in \mathbb{Q}$} \end{cases}\] – Ivan Koswara · 1 year, 9 months ago

Log in to reply

@Ivan Koswara – That's the exact correct answer! – Hobart Pao · 1 year, 9 months ago

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewest\[f : \mathbb{R} \to \mathbb{R}, \forall x f(x) = \begin{cases} 1 & \text{if $x \in \mathbb{Q}$} \\ -1 & \text{if $x \not\in \mathbb{Q}$} \end{cases}\] – Ivan Koswara · 1 year, 9 months ago

Log in to reply

– Hobart Pao · 1 year, 9 months ago

That's the exact correct answer!Log in to reply