Question

Let a,b and epsilon be elements of an ordered field a) show that if a<b+epsilon for...

Let a,b and epsilon be elements of an ordered field

a) show that if a<b+epsilon for every epsilon>0 then a<=b

b) use part a) to show that if |a-b|<epsilon for all epsilon>0 then a=b

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
Assume that (F,+,⋅) is a commutative field totally ordered. Given 3 elements a, b, c in...
Assume that (F,+,⋅) is a commutative field totally ordered. Given 3 elements a, b, c in F, prove that if a<b, then a+c<b+c. Prove that if 0<a<b, then b^{-1}<a^{-1}
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.
(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then...
(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then the equation ax+b=c has a unique solution. (b) If R is a commutative ring and x1,x2,...,xn are independent variables over R, prove that R[x σ(1),x σ (2),...,x σ (n)] is isomorphic to R[x1,x2,...,xn] for any permutation σ of the set {1,2,...,n}
let f(x) = 3x3 - 2 and let epsilon>0 be given Find a delta so that...
let f(x) = 3x3 - 2 and let epsilon>0 be given Find a delta so that |x -1 |<=delta implies |f(x) -1|<=epsilon
Let V be a vector space with ordered basis B = (b1, . . . ,...
Let V be a vector space with ordered basis B = (b1, . . . , bn). Does the basis having n elements imply that V is the coordinate space R^n?
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 ⊂...
Use an epsilon-delta argument to show f(x) = 2x^2 - 1 is continuous at every a...
Use an epsilon-delta argument to show f(x) = 2x^2 - 1 is continuous at every a ∈ ℝ.
18-5 A self-inductance L, a resistance R, and a battery of emf epsilon b are all...
18-5 A self-inductance L, a resistance R, and a battery of emf epsilon b are all connected in series. Use energy considerations to show that the current i satisfies the differential equation L (di/dt) + Ri = epsilon b. Now assume that i tidak sama dengan 0 and the battery is switced out of the circuit. Solve the resulting equation and find the relaxation time of this system.
Let R be a commutative ring with unity. Let A consist of all elements in A[x]...
Let R be a commutative ring with unity. Let A consist of all elements in A[x] whose constant term is equal to 0. Show that A is a prime ideal of A[x]
Let E be a field of characteristic p, where p is a prime number. Show that...
Let E be a field of characteristic p, where p is a prime number. Show that for all x, y that are elements of E, we have (x + y)^p =x^p + y^p, and hence by induction, (x + y)^p^n = x^p^n + y^p^n .
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT