Question

Asked Aug 27, 2019

17 views

_{α}}_{α∈A} is a collection of open intervals that are mutually disjoint: If α_{1} ≠ α_{2}, then I_{α1} ∩ I_{α2} = ∅. Prove or disprove: A must be at most countable.

Step 1

Consider the given information:

The collection {{I_{α}}, where α belongs to A} of open intervals that are mutually disjoint.

Now, let S be the union of all such disjoint open interval:

Step 2

Since, all intervals are mutually disjoint, so above mentioned collection is a disjoint collection.

Now, to show that they form a countable collection:

Let {*x*1,* x*2,* x*3, ….} denote the countable set of rational numbers. In each interval say, I*x* there will be infinitely many *x*, but among these there will be exactly one with...

Tagged in

Q: Pls explain to me step by step. Pls dont skip ay steps. thanks

A: Suppose P=(x0,y0) is an critical point of the system x\'=f(x,y) , y\'=g(x,y),and that f and g are di...

Q: Solve the given initial value problem by using the method of exactness. xy dx+(2x2+3y2-20)dy=0, y(0...

A: First identify M and N and check that the differential equation is exact.

Q: See attachment for question.

A: Click to see the answer

Q: pls explain to me step by step. pls write clearly and dont skip any steps. thanks

A: To test the contraction mapping property for the same operator T in two different settings . (C[0,1]...

Q: Show that x^2 + x + 1 has a zero in some extension field of Z_2 that is a simple extension.

A: To show that the polynomial x2 +x+1 has a zero in some extension of Z2 :First let if possible, α be ...

Q: 6.3.22 How many permutations of the letters ABC DEF GH contain D the string AB, DE, and BED?

A: The given letters are ABCDEFGH.Obtain the permutations as follows.

Q: Show that if charL(x) has a non-zero root, then for all m>0 we have Lm≠0. Explain what this means...

A: To relate non-zero eigenvalues and the characteristic polynomial of a linear operator

Q: See picture below: Please label answer clearly. Use the ~ symbol for the transformed function above ...

A: To establish the required properties of the Fourier transform of a general function f(t)

Q: For any sets A, B, and C, prove that Ac Bnc if and only if A c B and A CC

A: Consider the statement,