Question

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.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

If p and q are irrational numbers then may or may not be irrational. For example let . Then , which is rational.

Even if we consider . Let and . Then , which is rational.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
If p is a rational # and q is an irrrational # Is the number p/q...
If p is a rational # and q is an irrrational # Is the number p/q rational or irrational and prove your answer.
(1) Let x be a rational number and y be an irrational. Prove that 2(y-x) is...
(1) Let x be a rational number and y be an irrational. Prove that 2(y-x) is irrational a) Briefly explain which proof method may be most appropriate to prove this statement. For example either contradiction, contraposition or direct proof b) State how to start the proof and then complete the proof
Prove the following: (By contradiction) If p,q are rational numbers, with p<q, then there exists a...
Prove the following: (By contradiction) If p,q are rational numbers, with p<q, then there exists a rational number x with p<x<q.
Irrational Numbers (a) Prove that for every rational number µ > 0, there exists an irrational...
Irrational Numbers (a) Prove that for every rational number µ > 0, there exists an irrational number λ > 0 satisfying λ < µ. (b) Prove that between every two distinct rational numbers there is at least one irrational number. (Hint: You may find (a) useful)
If p is a rational number and q is an irrrational number Is the number p/4...
If p is a rational number and q is an irrrational number Is the number p/4 + q/5 rational or irrational and prove your answer.
3. Assume √2 ∈R. Let S = { rational numbers q : q < √2 }....
3. Assume √2 ∈R. Let S = { rational numbers q : q < √2 }. (a)(i) Show that S is nonempty. (ii) Prove that S is bounded from above, but is not bounded from below. (b) Prove that supS = √2.
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?
Find two rational numbers and two irrational numbers between 1.41 and (square root of 2), Clearly...
Find two rational numbers and two irrational numbers between 1.41 and (square root of 2), Clearly identify which are rational and which are irrational and explain in detail. Minimum of 1 paragraph..
Prove that between any two rational numbers there is an irrational number.
Prove that between any two rational numbers there is an irrational number.
Prove, that between any rational numbers there exists an irrational number.
Prove, that between any rational numbers there exists an irrational number.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT