I've seen many definitions of continuous functions. They all describe x in a domain, but there's not really much explanation about the domain considerations beyond examples with "all the reals" and "an interval of the reals." I'm trying to figure out what continuity would mean on a missing strip plane. For example, we know that [itex]f(x) = x [/itex] is a continuous function on the reals. But consider a missing strip plane where the interval [itex]x \in (0, 1][/itex] is missing. Is this function still continuous on that domain. Thanks!