Question

Hi, have a question regarding the continuity of the Sign function. It's commonly known that the sign function is discontinuous at x = 0 simply because of the way it is defined. However, is it then still discontinuous if the domain is R \ {0}? Why then?

Answer 1

this is sign function. So if you take out {0} nothing is fixed.

Answer 2

def of continuity in "0" for a function f is : lim x->0 f(x) = f(0). here, f(0) doesn't exist, so cannot be continuous on R/{0}

Answer 3

but in any case would the sign function then still be continuous in all R\{0}?

Answer 4

no