Defining 'Undefined'Date: 09/15/2003 at 21:21:13 From: Mike Subject: Is a hole in a graph (of a function) undefined? I know that division by zero is undefined, and can be graphed as an asymptote. Is a hole in the graph (an open circle) undefined also? Or is it called something else like 'non-existent'? I know they are both discontinuities. If a function is 'undefined at x', should I think of all discontinuities, or just vertical asymptotes, or are there more ways for it to be undefined? This isn't an important question (and it's kind of picky), so feel free to skip it if you are busy. Thanks. Date: 09/15/2003 at 23:01:23 From: Doctor Peterson Subject: Re: Is a hole in a graph (of a function) undefined? Hi, Mike. Why do you draw a hole in a graph? Because the function has no value for that x, right? And that is what "undefined" means. The function is not defined for that x. I get the impression that many students (and teachers, too) miss the simple meaning of "undefined", and imagine that it is some magical state like "infinity", rather than merely meaning that something is not defined, or does not exist. For that reason, I don't consider this a "picky" question at all; it's very important! Asking where a function is undefined is essentially just asking for the complement of its domain, which means any place it "lets light through" onto the x axis, hole or otherwise. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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