Talk:Continuous function
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I removed this:
- There are two types of discontinuity. A removable discontinuity can be drawn as if it were continuous, should one redefine f(c). A nonremovable discontinuity cannot be drawn as a "continuous line", even if f(c) is redefined. For example: if f(x) = (x² - 1) / (x - 1); then, f(x) has a removable discontinuity at x = 1 (which can be removed by defining f(1) soas to equal the limit of f(x), which is 2). On the other hand, if f(x) = 1 / x; then, f(x) has a nonremovable discontinuity at x = 0. (see also: division by zero).
The two given functions are continuous. This seems to be more relevant to removable mathematical singularity. AxelBoldt 19:49 20 Jun 2003 (UTC)
- If two functions f and g are continuous, then f + g and fg are continuous. If g(x) ≠ 0 for all x in the domain, then f/g is also continuous.
Even if g(x) is zero in a few points (a few == not all), (f/g)(x) can be defined for the points where g(x) ≠ 0. Won't this function be continuous too ?
- The zeroes of g can be any closed set, however complicated. It is better to say something simple, and true. Charles Matthews 18:53, 18 May 2004 (UTC)
There seems to be some inconsistency between the definition given and properties on the one hand, and the examples on the other. Is the tangent function, which presumably quilifies as a trigonometric function, to be considered continuous? I'm not sure what to say about logarithm. Josh Cherry 02:25, 3 Dec 2004 (UTC)