Question

Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show...

Let X be a subset of the integers from 1 to 1997 such that |X|≥34. Show that there exists distinct a,b,c∈X and distinct x,y,z∈X such that a+b+c=x+y+z and {a,b,c}≠{x,y,z}.

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
Prove that from any set A which contains 138 distinct integers, there exists a subset B...
Prove that from any set A which contains 138 distinct integers, there exists a subset B which contains at least 3 distinct integers and the sum of the elements in B is divisible by 46. Show all your steps
Suppose K is a nonempty compact subset of a metric space X and x∈X. Show, there...
Suppose K is a nonempty compact subset of a metric space X and x∈X. Show, there is a nearest point p∈K to x; that is, there is a point p∈K such that, for all other q∈K, d(p,x)≤d(q,x). [Suggestion: As a start, let S={d(x,y):y∈K} and show there is a sequence (qn) from K such that the numerical sequence (d(x,qn)) converges to inf(S).] Let X=R^2 and T={(x,y):x^2+y^2=1}. Show, there is a point z∈X and distinct points a,b∈T that are nearest points to...
Let X be a topological space and A a subset of X. Show that there exists...
Let X be a topological space and A a subset of X. Show that there exists in X a neighbourhood Ox of each point x ∈ A such that A∩Ox is closed in Ox, if and only if A is an intersection of a closed set with an open set.
Let Y be a subspace of X and let S be a subset of Y. Show...
Let Y be a subspace of X and let S be a subset of Y. Show that the closure of S in Y coincides with the intersection between Y and the closure of S in X.
let A be a subset of Rn and let x be a point in Rn. Show...
let A be a subset of Rn and let x be a point in Rn. Show that x is a limit point of A if and only if every open ball about x contains a point of A that is not equal to x
Let Z be the set of integers. Define ~ to be a relation on Z by...
Let Z be the set of integers. Define ~ to be a relation on Z by x~y if and only if |xy|=1. Show that ~ is symmetric and transitive, but is neither reflexvie nor antisymmetric.
Let f, g : X −→ C denote continuous functions from the open subset X of...
Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following: (a) The sum f+g is a continuous function. (b) The product fg is a continuous function. (c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.
Let A be a set and x a number. Show that x is a limit-point of...
Let A be a set and x a number. Show that x is a limit-point of A if and only if there exists a sequence x1 , x2 , . . . of distinct points in A that converges to x.
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 S = {x ∈ Z : −60 ≤ x ≤ 59}. (a) Which integers are...
Let S = {x ∈ Z : −60 ≤ x ≤ 59}. (a) Which integers are both in S and 6Z? (b) Which integers in S have 1 as the remainder when divided by 6? (c) Which integers in S are also in −1 + 6Z? (d) Which integers satisfy n ≡ 3 mod 6?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT