Amaton

Just wondering, but suppose [math]f(x)=\dfrac{a(x)}{b(x)}[/math]. If both [math]a(x)[/math] and [math]b(x)[/math] are each represented by their own infinite series, can I condense the function for both series into one sum and call it [math]f(x)[/math]?

I'm no physicist by any means, but I have to ask... Do you have a distaste for mathematical formulation? If so, to me that earns you some discredit. It's not simply "maths and diagrams and funny looking symbols". It's the laws of our universe as provided in our most accepted models. If you don't know the math, you'll never truly understand the theory.

Okay. Thanks a lot for the help.

Okay. That makes sense. I was just confused earlier from the misunderstanding. So to sum it up, I should be able to prove this using an epsilon-delta approach for an arbitrary [math]x[/math], which represents all [math]x[/math] in the interval [math]I[/math] (right?).

Sorry to revive a month-old thread, but I was just reading along and found this topic really interesting. EDIT: Okay, nevermind! Had a question about a certain proof, but I missed the obvious...

Okay, I think there's a misunderstanding here on my part. You say to pick an arbitrary point and evaluate its continuity. I first took this to mean taking some random, specific point and evaluating the continuity for just that one, specific point in the interval. But I don't see how that works for this... So I'm guessing you're talking about an arbitrary point for the interval in general?

Same no-sense subject, presented by the same individual, on multiple forums, garnering the same responses. Overlapping two planar figures and seeing the resulting number of sides is not the same as adding two numbers...

Ever tried riding with your hands to your sides? Good for about 2 seconds until you feel the bike start to shift and reflexively grab the handles again. The bike would've fallen if you had not acted so quickly, but thankfully you did and it did not fall. So I agree that it's simply the rider conducting its movement.

Okay, that makes sense. But I'm a little confused with this part: "pick an arbitrary number [math]x \in [a,b][/math] and show that the function [math]f[/math] is continuous at that point". Is this suggesting that showing a single point being continuous shows something about the entire interval? Could I also just exclusively look for discontinuities in the interval, where I can come to a conclusion based on a presence or lack thereof? I thought as much. Thanks.

Before I start, just want to say that this is not homework. I'm studying single-variable calculus and I sometimes have trouble getting certain things. (btw, might have more questions after this one) So. Let's say I have a function [math]f(x)[/math]. I'm aware that one can show it is continuous at a certain point, but how do I prove that it's continuous on an interval, say [math][a, b][/math]?

Hi everyone. Chose "Amaton" as my name for a fictional being I thought of. Doesn't matter how you pronounce it in your head, "uh-MAH-ton" or "AMA-tahn" is fine. Whatever suits your fancy. Anyway, I'm a young, scientifically-minded student aspiring to achieve pinnacle knowledge so that I can one day contribute to the world in a positive way. My main focus right now is independently studying mathematics. And as I'm relatively young, I have not yet taken formal classes for mathematics beyond high school. So I'll be asking a lot of questions in the math sub-forum. So yeah! I look forward to learning and contributing to the community here