math problem

[iwfc87]

Hey guys, well, my math problem is below and I need help on it:

 

Determine the maximal subset of R(real numbers) on which the following functions are (i) defined (ii) continuous

[math] [x] [/math] is a Gauss bracket of [math] x [/math]. Defined to be the greatest integer (Z) not greater than [math] x [/math]. Eg: x=1.7, [x]=1

[matt grime]

defined on what?

[iwfc87]

Hence I am clueless.

The subject is Calculus & Linear algebra and I think it's talking about functions (limits, continuity, blah blah blah).

 

It might mean defined function?

[matt grime]

Don't worry, I was trying to amke a point: part of the definition of function is its domain; seems like you have a poorly written maths book (don't worry, most of them are). In this sense just remember that you can only take square roots of positive numbers.

 

If you don't know what it's asking though, how do you expect ot find the answer? what is the definition of continuous?

[iwfc87]

Well, a continous function at a point is one at which the point is an element of the domain and the limit is equal to that of a function,

 

but the question I *think* means the function as a whole, which I'm not sure of. As far as my knowledge go (baby knowledge) a function is continuous if you can draw it without raising your pen, but that's does not suffice I don't think.

 

Apparently part (b) involves the "squeeze thereom" according to the lecturer, but I'm not too sure as I don't see what the function is being "squeezed" in between.

 

Cheers.

[matt grime]

a function is continuous if it is continuous at every point. therefore to show it is not continuous you need to find one point where it is not continuous. please, forget the raising your pen nonsense.