Question

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.

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 for all real numbers x, if x 2 is irrational, then x is irrational.
Prove that for all real numbers x, if x 2 is irrational, then x is irrational.
Prove or disprove the following statements. Remember to disprove a statement you have to show that...
Prove or disprove the following statements. Remember to disprove a statement you have to show that the statement is false. Equivalently, you can prove that the negation of the statement is true. Clearly state it, if a statement is True or False. In your proof, you can use ”obvious facts” and simple theorems that we have proved previously in lecture. (a) For all real numbers x and y, “if x and y are irrational, then x+y is irrational”. (b) For...
(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
In the style of the proof that square root of 2 is irrational, prove that the...
In the style of the proof that square root of 2 is irrational, prove that the square root of 3 is irrational. Remember, we used a proof by contradiction. You may use the result of Part 1 as a "Lemma" in your proof.
1) Prove that for all real numbers x and y, if x < y, then x...
1) Prove that for all real numbers x and y, if x < y, then x < (x+y)/2 < y 2) Let a, b ∈ R. Prove that: a) (Triangle inequality) |a + b| ≤ |a| + |b| (HINT: Use Exercise 2.1.12b and Proposition 2.1.12, or a proof by cases.)
Use proof by contradiction to prove the statement given. If a and b are real numbers...
Use proof by contradiction to prove the statement given. If a and b are real numbers and 1 < a < b, then a-1>b-1.
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)
Define f: R (all positive real numbers) -> R (all positive real numbers) by f(x)= sqrt(x^3+2)...
Define f: R (all positive real numbers) -> R (all positive real numbers) by f(x)= sqrt(x^3+2) prove that f is bijective
Prove the statement For all real numbers x, if x − ⌊x⌋ < 1/2 then ⌊2x⌋...
Prove the statement For all real numbers x, if x − ⌊x⌋ < 1/2 then ⌊2x⌋ = 2⌊x⌋.
Let E⊆R (R: The set of all real numbers) Prove that E is sequentially compact if...
Let E⊆R (R: The set of all real numbers) Prove that E is sequentially compact if and only if E is compact
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT