- #1

cmajor47

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## Homework Statement

Prove that the function defined as f(x)= x when x is rational and -x when x is irrational is only continuous at 0.

## Homework Equations

## The Attempt at a Solution

I have been looking at this website which proves this:

http://planetmath.org/encyclopedia/FunctionContinuousAtOnlyOnePoint.html

I don't understand how the writer proves that the function is not continuous when a[tex]\neq[/tex]0.

Why do they take x

_{k}= to something? How does this help them show that the limits equal a and -a.

How does showing that prove that f is not continuous at a?

I know those are a lot of question, but maybe an answer to even just the first ones would help me understand this proof.

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