For MA 225, we are suppose to Grade these examples in the book. If the claim is false, the proof is an F. The claim for this one says "Every real function is continuous at x=0". Looking at the following proof they provided is long and looks bad. But can I clearly state that the claim is false by the fact that an integer over X is not continuous at x=0. Mainly, is 8/x or a/x a real function?

2/13/2007 7:07:06 PM

Yeah, your counterexample is right. Just say the proof they give is unnecessary and can be disproved with the following counterexample., 1/x at x=0.

2/13/2007 7:22:19 PM

go ahead and give that counter example. But, you're going to need to show (by using the definition or appropriate thm.) that your example is indeed not continuous at x=0. Being MA225 probably use the epsilon-delta definition or sequence based definition of cont' fc'n.

you could probably find an easier example, e.g. f(x)=0 if x<=0 and f(x)=1 if x>0.

[Edited on February 13, 2007 at 7:33 PM. Reason : or whatever]

Quote :

"Mainly, is 8/x or a/x a real function?"

your textbook should provide the definition of a real function.

Quote :

"The claim for this one says "Every real function is continuous at x=0". Looking at the following proof they provided is long and looks bad. "

If I understand this right, they are making a false claim and then attempting to "prove" it by using an invalid proof. Probably logical fallacy. Your objective is to read through the proof, find where they made the error and then provide your counter example. Again as I said above, you must prove your counter example-- you can't just state it. I mean *maybe* in higher level classes if the counter example is really trivial, but not when the whole point is learning arguments and proof techniques.

[Edited on February 13, 2007 at 7:45 PM. Reason : .]

2/13/2007 7:32:46 PM