Question

Let N2K be the set of the first 2k natural numbers. Prove that if we choose...

Let N2K be the set of the first 2k natural numbers. Prove that if we choose k + 1 numbers out of these 2k, there is at least one pair of numbers a, b for which a is divisible by 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
Exercise 6.6. Let the inductive set be equal to all natural numbers, N. Prove the following...
Exercise 6.6. Let the inductive set be equal to all natural numbers, N. Prove the following propositions. (a) ∀n, 2n ≥ 1 + n. (b) ∀n, 4n − 1 is divisible by 3. (c) ∀n, 3n ≥ 1 + 2 n. (d) ∀n, 21 + 2 2 + ⋯ + 2 n = 2 n+1 − 2.
Let S = {0,1,2,3,4,...}, A = the set of natural numbers divisible by 2, and B...
Let S = {0,1,2,3,4,...}, A = the set of natural numbers divisible by 2, and B = the set of numbers divisible by 5. What is the set A intersection B? What is the set A union B? Please show your work.
Let S(n) be a monotonic non-decreasing positive function defined for all natural numbers n. We do...
Let S(n) be a monotonic non-decreasing positive function defined for all natural numbers n. We do not know the value of S(n) for every n ∈ N except when n = 2k for some k ∈ N, in which case S(n) = n log n + 3n − 5. Show that S(n) ∈ Θ(n log n). Hint: (if you use it, you need to prove it): ∀n > 1 ∈ N, ∃k ∈ N, such that 2k-1 ≤ n ≤...
Let S(n) be a monotonic non-decreasing positive function defined for all natural numbers n. We do...
Let S(n) be a monotonic non-decreasing positive function defined for all natural numbers n. We do not know the value of S(n) for every n ∈ N except when n = 2k for some k ∈ N, in which case S(n) = n log n + 3n − 5. Show that S(n) ∈ Θ(n log n). Hint: (if you use it, you need to prove it): ∀n > 1 ∈ N, ∃k ∈ N, such that 2k-1 ≤ n ≤...
Let S(n) be a monotonic non-decreasing positive function defined for all natural numbers n. We do...
Let S(n) be a monotonic non-decreasing positive function defined for all natural numbers n. We do not know the value of S(n) for every n ∈ N except when n = 2k for some k ∈ N, in which case S(n) = n log n + 3n − 5. Show that S(n) ∈ Θ(n log n). Hint: (if you use it, you need to prove it): ∀n > 1 ∈ N, ∃k ∈ N, such that 2k-1 ≤ n ≤...
If we let N stand for the set of all natural numbers, then we write 6N...
If we let N stand for the set of all natural numbers, then we write 6N for the set of natural numbers all multiplied by 6 (so 6N = {6, 12, 18, 24, . . . }). Show that the sets N and 6N have the same cardinality by describing an explicit one-to-one correspondence between the two sets.
Let A be the set of all natural numbers less than 100. How many subsets with...
Let A be the set of all natural numbers less than 100. How many subsets with three elements does set A have such that the sum of the elements in the subset must be divisible by 3?
Let m = 2k + 1 be an odd integer. Prove that k + 1 is...
Let m = 2k + 1 be an odd integer. Prove that k + 1 is the multiplicative inverse of 2, mod m.
1. (a) Let S be a nonempty set of real numbers that is bounded above. Prove...
1. (a) Let S be a nonempty set of real numbers that is bounded above. Prove that if u and v are both least upper bounds of S, then u = v. (b) Let a > 0 be a real number. Define S := {1 − a n : n ∈ N}. Prove that if epsilon > 0, then there is an element x ∈ S such that x > 1−epsilon.
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....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT