Why is the characteristic function* of a ball in R(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}continuous everywhere except on its surface?My lecturer said that a circle is a 'set of discontinuities' - what exactly does that mean?

(some context: we're looking at how we can integrate over a ball. Previously we've only looked at Riemann integration over rectangles - for that, he also introduced the theory by first defining integrals for the characteristic function over rectangles).

*The characteristic function of any set in R^{n}was defined to be 1 if x was a point inside the set and 0 if t was outside

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Circle is a set of a discontinuities?

**Physics Forums | Science Articles, Homework Help, Discussion**