
Re: Nonstandard Analysis Continuity Question
Posted:
Oct 1, 2012 9:01 AM


In article <547d1b5caaaa4c2c9e97f28c86a6a724@x14g2000yqh.googlegroups.com>, <nonstandardanalysis@yahoo.com> wrote:
> On Sep 29, 7:46 pm, FredJeffries <fredjeffr...@gmail.com> wrote: > > On Sep 27, 8:04 pm, nonstandardanaly...@yahoo.com wrote: > > > > > Suppose we have a function f: *R > { 0, 1 } defined as f(x) = 1 if x > > > is limited, and f(x) = 0 if x is unlimited. Is f continuous? On one > > > hand it doesn't appear that f is continuous since the function jumps > > > from 0 to 1 without meeting any of the points in between. However, > > > there is no point of discontinuity. Since f is an external function, > > > Scontinuity doesn't apply. > > > > The discontinuity does not occur at a point. It occurs at a gap, like > > the function from the rationals to {0, 1} defined as > > g(x) = 1 if x^2 < 2 and g(x) = 0 if x^2 > 2 > > It didn't occur to me that a function could be continuous at every > point, but still not be continuous overall.
And what do you mean by "continuous overall"???
 G. A. Edgar http://www.math.ohiostate.edu/~edgar/

