Question

Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of...

Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of F}. Prove that infimum and supremum exist or do not exist.

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

Homework Answers

Answer #1

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
A. Let p and r be real numbers, with p < r. Using the axioms of...
A. Let p and r be real numbers, with p < r. Using the axioms of the real number system, prove there exists a real number q so that p < q < r. B. Let f: R→R be a polynomial function of even degree and let A={f(x)|x ∈R} be the range of f. Define f such that it has at least two terms. 1. Using the properties and definitions of the real number system, and in particular the definition...
Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be...
Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be the set of all linear combinations of a(x) and b(x). Let d(x) be the monic polynomial of smallest degree in S. Prove that d(x) divides a(x).
Let A, B be sets and f: A -> B. For any subsets X,Y subset of...
Let A, B be sets and f: A -> B. For any subsets X,Y subset of A, X is a subset of Y iff f(x) is a subset of f(Y). Prove your answer. If the statement is false indicate an additional hypothesis the would make the statement true.
Let E/F be a field extension, and let α be an element of E that is...
Let E/F be a field extension, and let α be an element of E that is algebraic over F. Let p(x) = irr(α, F) and n = deg p(x). (a) For f(x) ∈ F[x], let r(x) (∈ F[x]) be the remainder of f(x) when divided by p(x). Prove that f(x) +p(x)= r(x)+p(x)in F[x]/p(x). (b) Prove that if |F| < ∞, then | F[x]/p(x)| = |F|n. (For a set A, we denote by |A| the number of elements in A.)
Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}. 1. find...
Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}. 1. find the infimum and the supremum of S, and prove that these are indeed the infimum and supremum. 2. find all the boundary points of the set S. Prove that each of these numbers is a boundary point. 3. Is the set S closed? Compact? give reasons. 4. Complete the sentence: Any nonempty compact set has a....
Let F be a field and Aff(F) := {f(x) = ax + b : a, b...
Let F be a field and Aff(F) := {f(x) = ax + b : a, b ∈ F, a ≠ 0} the affine group of F. Prove that Aff(F) is indeed a group under function composition. When is Aff(F) abelian?
Let f and g be continuous functions from C to C and let D be a...
Let f and g be continuous functions from C to C and let D be a dense subset of C, i.e., the closure of D equals to C. Prove that if f(z) = g(z) for all x element of D, then f = g on C.
Real Analysis I Prove the following exercises (show all your work)- Exercise 1.1.1: Prove part (iii)...
Real Analysis I Prove the following exercises (show all your work)- Exercise 1.1.1: Prove part (iii) of Proposition 1.1.8. That is, let F be an ordered field and x, y,z ∈ F. Prove If x < 0 and y < z, then xy > xz. Let F be an ordered field and x, y,z,w ∈ F. Then: If x < 0 and y < z, then xy > xz. Exercise 1.1.5: Let S be an ordered set. Let A ⊂...
Let E be an extension of F, and let S be a subset of E.IfF(S) is...
Let E be an extension of F, and let S be a subset of E.IfF(S) is the subfield of E generated by S over F, in other words, the smallest subfield of E containing F and S, describe F(S) explicitly, and justify your characterization.
(2) Let X be a set and < a linear order on X. Let S be...
(2) Let X be a set and < a linear order on X. Let S be a subset of X. Show that if S has a least element, then S has a unique least element. (3) Give an example, where S has no least element. (Be sure to specify what X, < and S are!) (4) Let X be a set and < a linear order on X. Let S be a subset of X which is bounded below. Show...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT