Let B be a set of positive real numbers with the property thatadding together any finite subset of elements from B always gives a sum of 2 or less. Show B must be finite or countable.

Q: Determine the set of all real numbers x such that x-9 exists. x2-9

A: x-9x2-9

Q: count the number N of all sets A := {1, x2, X3, X4} of non-negative integers satisfying Xi + x2 +…

A:

Q: . Let a be a positive number. Prove that for each real number x there is an integer n such that na <…

A:

Q: Prove that the product of any k consecutive positive integers is an integer multiple of k!.

A:

Q: Use Cantor Diagonal Argument to prove that the set of all real numbers in the interval (2, 3) is…

A:

Q: If R is an integer domain, show that it contains exactly two elements a that satisfy a? = a.

A: Given R is an integral domain. We have to show that it contains exactly two elements a that satisfy…

Q: b) Use the idea in part (a) to determine an explicit one-to-one correspondence between zt and the…

A: as you asked only the solution for (b) , the solution of the part (b) is given below...

Q: Given the domain and codomain of set of all real numbers, categorize the ff.: f (x) = 2x³ – 4…

A: Given - The domain and codomain is the set of real numbers. Function given is f(x)=2x3-4 which can…

Q: What is the set Z+ of all positive integers?

A: Set of integers are represented as: ℤ={.....,-3,-2,-1,0,1,2,3.........} Set of natural numbers:…

Q: Determine integers x and y such that (а) gcd(51, 288) — 51х + 288у (b) gcd(357, 629) = 357x + 629y

A:

Q: Use a sequence of equivalences to prove that the following statement is true for all real numbers x:…

A: c) we have to prove x6≥4x3-4 ∀x∈IR if x=0 then 0≥-4    holdsat x=1 then 1≥0       holdsat x=2 then…

Q: Prove. If x is a negative real number, there exists an integer k such that k >= x.

A: x is a negative real number then  x &lt; 0 So that desired integer k = 0

Q: Let a and b be integers. Show that if every integer that divides a also divides b, then a | b. (a…

A:

Q: Let ? be a set of positive real numbers with the property that adding together any finite subset of…

A:

Q: R.4. Prove that the set of real numbers in the interval (0, 1) which have a terminating decimal…

A:

Q: Find a set B that is well-defined such that 10 ɛ B and 5 ɛ B. B = {x|x ɛl and x < 11}, I the set of…

A:

Q: Determine whether each of these sets is finite, countably infinite, or uncountable. For those that…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Abstract Algebra

A: To find non-negative representations under the given conditions

Q: -ん 2 kodd

A:

Q: Find all integer numbers a for which

A:

Q: The set A consists of nine positive integers, none of which has a prime divisor larger than six.…

A:

Q: Prove that every nonempty set of negative integers has a largest element.

A:

Q: Every none-empty subset of integer numbers contains a least element.

A:

Q: If all entries of A and A -1 are integers, prove that &lt;let A = 1 or -1. Hint: What is det A times…

A:

Q: Assume B is a closed subset of the real numbers. Prove that Bc = R−B is an open set.

A:

Q: Let A be the set of odd integers, and let B be the set of positive integers less than 10.  Find A∩B

A: our objective is to find A intersection B

Q: (5) Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x…

A: To prove: If x is any real number and any subset A of ℝ, then either x is an interior point of A or…

Q: take any 11 integers. prove that there must be at least two of them that differ by an integer…

A:

Q: Let X = {x;} be a set of n positive integers. Show that the sum of the integers of a subset of X is…

A: It is required to show that sum of elements of a subset of described set, X, is divisible by integer…

Q: Prove that the subset R/Q , the set of all irrational numbers , of R id of second category .

A:

Q: Show that for every real number ɛ 8 > 3ɛ. greater than zero, there exist a real number 8 such that

A:

Q: Prove that if a and b are integers such that a|b, then either a = b or a = -b

A: Take a = 2 ,b = 4 . We have a divides b but neither a = b , nor a = -b.

Q: Let A be a set of integers closed under subtraction. Prove that if A is nonempty, then 0 is in A.

A: Let A be a set of integers closed under subtraction. Prove that if A is nonempty, then 0 is in A.

Q: Let x be an element of the real numbers. Prove |x| is greater-than or equal to 0. State any theorems…

A: For any real number x , the absolute or modulus of x is denoted byx and is defined as x=x , if…

Q: The set of positive integers is ordered-isomorphic to the set of even positive integers. ylgn ihi

A: Given a statement

Q: 2. Determine all values of x - y when x and y are integers such that x = 360 + y².

A: The given equation is. x2=360+y2x2-y2=360x+yx-y=360 Since it is given that x and y are integers, so…

Q: Prove using Direct Proof: For all integers a,b and c if a|b and b|c then a|c

A:

Q: . Show that if r is a nonzero real number, k and m are distinct integers, and ax and am are any real…

A: Given system is Crk+kDrk=akCrm+mDrm=am also given that r is non-zero real number and k and m are…

Q: let S be the set of real numbers. if a,b is an element of S define a~b if a-b is an integer,show…

A:

Q: Consider the subsets ø (empty set) and R of the real numbers. Prove that both of these are open and…

A: Consider the set of real numbers ℝ. We know that a subset A of ℝ is open if for every x∈A, there…

Q: Suppose that A is a set of 10 natural numbers, all of which are less than 50. Show that A must have…

A:

Q: Prove that there are as many positive real numbers as there are real numbers.

A: Here , we have prove that all positive numbers are real numbers.

Q: Show that if a and b are integers such that a|b, then a^k|b^k for every positive integer k.

A:

Q: . Show that there exist no nonzero real numbers a and b such that va² + b? = Va³+b.

A: To remove the radical sign in the equation a2+b2=a3+b33, raise the power to 6 on both sides of the…

Q: 5. Determine whether the set of all ordered triples of real numbers with the op- erations defined…

A: Given: (x,y,z)+(x',y',z')=(x+x',y+y',z+z') k(x,y,z)=(x,1,z)

Q: (d) The set of all real numbers greater than 1 and less than 7.

A: A set builder notation is a set which consists of all the conditions a variable should satisfy.

Q: Suppose A is a set of real numbers such that 7EA and sup A >7. Must A contain a number grater than 7…

A:

Q: What is the set Z of all integers?

A: The set of all integers is, ℤ=........, -4, -3, -2, -1, 0, 1, 2, 3, 4, ........

Q: Suppose that S is not an empty set, and is a set of real numbers bounded below. Let A-1 be the set…

A: Bounded Above: A set A ⊂ R of real numbers is bounded from above if there exists a real number M ∈…