Question

Show that each non-empty open interval in R contains uncountably many irrational numbers

Show that each non-empty open interval in R contains uncountably many irrational numbers

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
prove that any open interval (a,b) contains infintly many rational numbers? use the completeness property of...
prove that any open interval (a,b) contains infintly many rational numbers? use the completeness property of R or Partition
Let T be the half-open interval topology for R, defined in Exercise 4.6. Show that (R,T)...
Let T be the half-open interval topology for R, defined in Exercise 4.6. Show that (R,T) is a T4 - space. Exercise 4.6 The intersection of two half-open intervals of the form [a,b) is either empty or a half-open interval. Thus the family of all unions of half-open intervals together with the empty set is closed under finite intersections, hence forms a topology, which has the half-open intervals as a base.
Prove the statement " For all real numbers r, if r is irrational, then r/2 is...
Prove the statement " For all real numbers r, if r is irrational, then r/2 is irrational ". You may use any method you wish. Be sure to state what method of proof you are using.
Consider a number line. How many rational numbers are there? How many irrational numbers? How are...
Consider a number line. How many rational numbers are there? How many irrational numbers? How are they separated? This is a very abstract concept, but will help when considering the graph. What is the definition of a rational number? Of an irrational number?
Let p and q be irrational numbers. Is p−q rational or irrational? Show all proof.
Let p and q be irrational numbers. Is p−q rational or irrational? Show all proof.
There are 6 closed boxes on the table. Two of them are non-empty, the rest 4...
There are 6 closed boxes on the table. Two of them are non-empty, the rest 4 are empty. You open boxes one at a time until you find a non-empty one. Let X be the number of boxes you open. (i) Find the probability mass function of X. (ii) Find E(X) and V ar(X). (iii) Suppose each non-empty box contains a $100 prize inside, but each empty box you open costs you $50. What is your expected gain or loss...
show that E is a finite open interval in R if and only if x +...
show that E is a finite open interval in R if and only if x + E is one. Then prove |E| = |x + E|.
Let x, y, z be three irrational numbers. Show that there are two of them whose...
Let x, y, z be three irrational numbers. Show that there are two of them whose sum is again irrational.
Finding the Mean The mean (or average) of a non-empty list of n numbers is the...
Finding the Mean The mean (or average) of a non-empty list of n numbers is the sum of the numbers divided by n. For example, the mean of 2, 7, 3, 9, and 13 is (2+7+3+9+13)/5, or 6.8. Write a function mean that takes as input a non-empty list of numbers (of any length > 0) and returns the mean.
Let A, B be non-empty subsets of R. Define A + B = {a + b...
Let A, B be non-empty subsets of R. Define A + B = {a + b | a ∈ A and b ∈ B}. (a) If A = (−1, 2] and B = [1, 4], what is A + B?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT