What is the Difference Between Rational and Irrational Numbers in Calculus?

[omagdon7]

I am a little terrified at the moment as my Calc 2 teacher both mumbles and has a heavy accent. Anyways this is what caused me the most anxiety about the first class could someone please explain to me wtf he was trying to say by this?

these are two piece-wise functions

F(x)
1 x irrational
0 x rational

G(x)

0 x irrational
-1 x rational

and the integration of F(x)-G(x)=1 so um could someone please explain what he meant by x rational and x irrational.

 

[arildno]

Whst he meant, was that F or G are NON-INTEGRABLE (are you sure what this means?)
but that F(x)-G(x) IS integrable (do you see why?).

 

[omagdon7]

I see that F and G by themselves are non-integrable but I don't understand why together they are. Is this some sort of like prep for limits and series in the future?

 

[Math Is Hard]

Chinese Calculus Professor

Oh, dear! Chinese Calculus is much, much harder than regular Calculus. I'm surprised you signed up for it.
But never fear - I'm sure arildno will help you sort it all out.

 

[omagdon7]

If I have the oppurtunity to transfer into another class with a professor who I feel more comfortable with would you advise it or should I just man up and get my Calculus 2 swerve on with Dr. Ho.

 

[Math Is Hard]

Honestly, I would transfer, especially if you are going further with math (and/or physics). You don't want any surprises coming up later because you didn't grasp the fundamentals.
Grade-wise, though, I have to say I have had the easiest time in classes with teachers who are non-native English speakers because they tend to pass out prodigious (test-related) lecture notes to compensate for the communication problems. But I don't know if this is the case with your teacher.
Essentially, I think it all depends on your goals.

 

[Chrono]

My computer science professor is chinese and he has a pretty heavy accent as well. I say give it a while and you'd learn to get used to it. Besides, you never know how many times you're going to have that same guy again. This will be my fourth semester having him.

 

[Manchot]

Yeah, I was worried about the same thing when I found out that my Calc III teacher had an extremely thick Russian accent. But like Chrono said, you get used to it.

 

[Math Is Hard]

I'll never forget the Indian computer sci teacher I had who spent the first class lecturing about 'waddy ables'. Eventually it clicked that he meant 'variables'.

 

[Chrono]

Mine refers to Java as "Jawa".

 

[Hurkyl]

It means that, if x is rational, then F(x) = 0. Similarly, if x is irrational, F(x) = 1. The normal notation for this sort of conditionally defined function is:

$$F(x) := \left\{ \begin{array}{ll} 0 \; & \text{x is rational} \\ 1 \; & \text{x is irrational} \end{array}$$

 

[matt grime]

Can I ask you to give the lecturer a break, speaking as someone who's had to teach in American classrooms. You are'nt an easy lot to teach and he's going to take a while ot get used to you too.

And finally, F(x)-G(x)=1, for all x, hence it is integrable.

(I'm presuming you do know what rational and irrational mean and that I'm mis reading one part of your post)

 

[omagdon7]

Yea after looking at it more carefully I understand it now it was just kind of unfamiliar. I ended up transferring out into another class. What worried me most was that the class grade was based solely on a couple of tests but anyways thanks all for your help.