Purchase Solution

# Real analysis

Not what you're looking for?

Let C be the Cantor set defined C=intersection sign on top inf bottom n=0 C_n.Define g:[0,1]->R by g(x)={1 if x belong to C and 0 if x does not belong to C.
a-show that g fails to be continuous at any point c belong to C.
b-prove that g is continuous at every point c does not belong to C.

##### Solution Summary

This is a proof regarding continuity and belonging to sets.

##### Solution Preview

Proof:

We know that the Cantor set C is a closed set with no interior points. So [0,1]-C is an open set.

a. For each point x in C, because x is not an interior point, then in any neiborhood ...

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.