Prove. For any x, y ∈ R and x < y, ⟨(x, y), ≤⟩ is not well-ordered, where (x, y) is an open interval and ≤ is the usual ordering.

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Q: Exercise 1.1.1 Show that the set of all continuous solutions of the differ- ential equation u"(x) +…

A: Answer given below.

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Q: Let us consider a function f which has only one zero in the interval [-2, 7]. How many iteration n…

A: The function f has only one zero in the interval -2,7

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Q: Let W be the set of vectors of the form a b A = where a, b, c are real numbers such C that 8b + 3a…

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Q: 24. If P(An) ≥ e > 0, for all large n, then P (An i.o.) ≥ €.

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Q: Let R = ({0, 1,,8), 0, 0) be a ring where and are defined as follows: a b = (a + b) mod 9 a Ob= (ab)…

A: Using the definition of the Ring R we answer all the questions. Important thing to note is the using…

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Q: 2) Which of the following is a separable differential equation obtained by applying the appropriate…

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Q: If u and v are vector-valued functions of the variablet and u(2) = (1,0,1), v(2) = (0,2,0), u'…

A: Let rt→=u×v Hence rt'→=u'×v+u×v' at t=2 r2'→=u'2×v2+u2×v'2

Q: Perform the following congruence computations. Make sure that the number you enter is 20 and ≤N-1,…

A: (a) 5946+7925≡        mod 45⇒13871≡        mod 454530813871-13500371-360011∴5946+7925≡  11      mod…

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A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: f(x)= a. Determine the Fourier series for the periodic function: -2, when -π <x<0 +2, when 0<x<π…

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Q: Prove that a group of order 28 must have an element of order 2.

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Q: A. Determine whether the vector v is in the span of a set S, where v = (2-1 13) and S = {( 1 0 1…

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Q: A coin is tossed three times, where (i) A: head on third toss, B: heads on first two tosses (ii) A:…

A: Solution of the question is given below.

Q: Base on the data below solve for the required values. x 53 47 41 50 58 62 45 60 y 5 5 7 4 10 12 3 11…

A: x 53 47 41 50 58 62 45 60 y 5 5 7 4 10 12 3 11

Q: -4 7 3 -56 Given v = 3 3 a -10 ܠ ' -6 find the closest point to in the subspace W spanned by -6 and

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A: Consider the case where there are n identical things to be distributed among k . Total no. of ways =…

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Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

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Q: 1 1.3 1 Question 2. + + 3.5 1 5.7 + ... + 1 (2n-1) (2n + 1) for n ≥ 1

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Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

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Q: The three vectors Ot + 11, v₂ = 3t² + 14t + 10, v3 = -1² + 4t + x + 1 of early dependent if x =

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Q: Find a general Solution to the given equation for to E²Y" (t)-ty' (t) + 47 (E) = 0 7 The general…

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Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

A: Since we know that ℝ is a complete metric space. so, In complete metric space every Cauchy sequence…