Question

Prove that for every x ∈ R \ Q, the set Ax = {qx | q...

Prove that for every x ∈ R \ Q, the set Ax = {qx | q ∈ Q} is dense in R.

please prove with dense property.

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
4. Prove that {(x, y) ∈ R 2 ∶ x − y ∈ Q} is an...
4. Prove that {(x, y) ∈ R 2 ∶ x − y ∈ Q} is an equivalence relation on the set of real numbers, where Q denotes the set of rational numbers.
[Q] Prove or disprove: a)every subset of an uncountable set is countable. b)every subset of a...
[Q] Prove or disprove: a)every subset of an uncountable set is countable. b)every subset of a countable set is countable. c)every superset of a countable set is countable.
Prove using rules of inference: ?(?indy) ∀x(S(x) <-> Q(x)) ∀x(Q(x) ʌ R(x)) R(Cindy)
Prove using rules of inference: ?(?indy) ∀x(S(x) <-> Q(x)) ∀x(Q(x) ʌ R(x)) R(Cindy)
let F : R to R be a continuous function a) prove that the set {x...
let F : R to R be a continuous function a) prove that the set {x in R:, f(x)>4} is open b) prove the set {f(x), 1<x<=5} is connected c) give an example of a function F that {x in r, f(x)>4} is disconnected
1. Prove p∧q=q∧p 2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers .3. Prove...
1. Prove p∧q=q∧p 2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers .3. Prove R∪(S∩T) = (R∪S)∩(R∪T). 4.Consider the relation R={(x,y)∈R×R||x−y|≤1} on Z. Show that this relation is reflexive and symmetric but not transitive.
Prove: If D = Q\{3}. R = Q\{-3}, and f:D-> R is defined by f(x) =...
Prove: If D = Q\{3}. R = Q\{-3}, and f:D-> R is defined by f(x) = 1+3x/3-x for all x in D, then f is one-to-one and onto.
Recall that Q+ denotes the set of positive rational numbers. Prove that Q+ x Q+ (Q+...
Recall that Q+ denotes the set of positive rational numbers. Prove that Q+ x Q+ (Q+ cross Q+) is countably infinite.
Prove that the following arguments are invalid. 1. (∃x) (Ax * ~Bx) 2. (∃x) (Ax *...
Prove that the following arguments are invalid. 1. (∃x) (Ax * ~Bx) 2. (∃x) (Ax * ~Cx) 3. (∃x) ( ~Bx * Dx) / (∃x) [Ax *(~Bx * Dx)]
Prove the division algorithm for R[x]. Where R[x] is the set of real polynomials.
Prove the division algorithm for R[x]. Where R[x] is the set of real polynomials.
Solve the following pair of simultaneous equations for x and y. qx+ (1− p)y = R...
Solve the following pair of simultaneous equations for x and y. qx+ (1− p)y = R and px+ (1−q)y = S.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT