Homework Answers
1/13 has tertiary representation 0.002002002....
Since such a representation doesn't contain 1 and we know that all digits between 0 and 1 not containing 1 in their tertiary representation belong in the cantor set
So we can say that 1/13 does lie in the cantor set
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1. Determine whether is in the Cantor set. 2. Prove Property 6 of the Cantor set. 1. Determine whether is in t...
Please answer question 2.84 and 2.85. - page ou. 2.84 Prove that the Cantor set, P,...
Please answer question 2.84 and 2.85.
- page ou. 2.84 Prove that the Cantor set, P, has measure zero. Hint: Recall that PCP for each neN, where Pn is the set remaining after the nth step in the construction of the Cantor set. 2.85 Show that a subset of a set of measure zero also has measure zero. *2.86 Prove that a nendegenerato intoul 1
Use Cantor Diagonal Argument to prove that the set {?∈ℝ|9≤?<10} is uncountable infinite.
Use Cantor Diagonal Argument to prove that the set {?∈ℝ|9≤?<10} is uncountable infinite.
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1,...
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...
(Real Analysis) Please prove for p=3 case with details. Cantor set and Cantor ternary function Properties of Ck o C is closed Proposition 19 C is closed, uncountable, m(C) 0 p-nary expansion Let r...
(Real Analysis)
Please prove for p=3 case with details.
Cantor set and Cantor ternary function Properties of Ck o C is closed Proposition 19 C is closed, uncountable, m(C) 0 p-nary expansion Let r E (0,1) and p a natural number with p as 1. Then r can be written where a e (0,1,2.. ,p-1) r- p" Proof for p 3 case: HW 36 Cantor set and Cantor ternary function Unique expression when p 3 x E (0, 1), p-3...
1. The Cantor set is one of the most famous sets in mathematics and has some rather unique proper...
Please show all the work!!! Thank you
1. The Cantor set is one of the most famous sets in mathematics and has some rather unique properties. The Cantor set was discovered in 1874 by Henry John Stephen Smith and introduced to the world by George Cantor in 1883. The Cantor set is a set of points lying on a single closed line segment, say from [0,1]. It is constructed as follows: Start with the closed interval Co-10.1]. Remove the open...
(6 pts) 3. Prove whether or not the set of ordered pairs of the form (w...
(6 pts) 3. Prove whether or not the set of ordered pairs of the form (w ) is a subspace of R'. (6 pts) 4. Prove whether or not the set of polynomials of the form a+Ox+ax is a subspace of P. 5. Let S = {(2,2,1,6),(1,3,5,1),(1,7,14,-3)} . (6 pts) Is S linearly independent or linearly dependent? (3 pts) b. Find (4 pts) 6. Give three examples of vectors in the span of {0.2.1),(3.1.0);
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether...
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether they form a basis of the vector space to which they belong. s 10110 -1 ) / -1 2) / 2 1 17 ) } in M2x2(R). "11-21 )'(1 1)'( 10 )'(2 –2 )S (b) {23 – X, 2x2 +4, -2x3 + 3x2 + 2x +6} in P3(R) (the set of polynomials of degree less than 3. (c) {æ4—23+5x2–8x+6, – x4+x2–5x2 +5x-3, x4+3x2 –...
Consider the construction of the Cantor set C c [0, 1] In the st step we...
Consider the construction of the Cantor set C c [0, 1] In the st step we remove the open interval (, ) ad are left with two closed intervals [0· and [릎,1]. Let J1 denote one of these two closed intervals. In the 2nd step, we divide J into three intervals and remove the open middle third interval. We are left with two closed intervals inside J. Let J2 denote one of these two intervals. For example, if Ji were...
Exercise 6.8. Recall the geometric description of the Cantor set. With Ko:-[0, 1], we constructed...
Exercise 6.8. Recall the geometric description of the Cantor set. With Ko:-[0, 1], we constructed i Go(o) UG2(o). With d) the distance defined in (2), what is d(Ko,K1)? For any k e N, what is d(KkKo) and d(k,Kk+1)? (10 pts)
Exercise 6.8. Recall the geometric description of the Cantor set. With Ko:-[0, 1], we constructed i Go(o) UG2(o). With d) the distance defined in (2), what is d(Ko,K1)? For any k e N, what is d(KkKo) and d(k,Kk+1)? (10 pts)
4. (6 pt) Determine whether or not each set of vectors is a basis for R....
4. (6 pt) Determine whether or not each set of vectors is a basis for R. Justify your answer you can determine the answer without calculation, say which basis property is guaranteed to fin and how you know that the property fails. (a) {(1,2,3), (4,5,6),(1,1,2),(-3,5,7)}. (b) {(0,2,5), (1,2,3), (0,3,4)}
Please answer question 2.84 and 2.85.
- page ou. 2.84 Prove that the Cantor set, P, has measure zero. Hint: Recall that PCP for each neN, where Pn is the set remaining after the nth step in the construction of the Cantor set. 2.85 Show that a subset of a set of measure zero also has measure zero. *2.86 Prove that a nendegenerato intoul 1
1. Determine whether the following set is linearly independent or not. Prove your clas a. [1+1, 2+2-2,1 +32"} b. {2+1, 3x +3',-6 +2"} 8. Let T be a linear transformation from a vector space V to W over R. . Let .. . be linearly independent vectors of V. Prove that if T is one to one, prove that (un)....(...) are linearly independent. (m) is ) be a spanning set of V. Prove that it is onto, then Tu... h...
(Real Analysis)
Please prove for p=3 case with details.
Cantor set and Cantor ternary function Properties of Ck o C is closed Proposition 19 C is closed, uncountable, m(C) 0 p-nary expansion Let r E (0,1) and p a natural number with p as 1. Then r can be written where a e (0,1,2.. ,p-1) r- p" Proof for p 3 case: HW 36 Cantor set and Cantor ternary function Unique expression when p 3 x E (0, 1), p-3...
Please show all the work!!! Thank you
1. The Cantor set is one of the most famous sets in mathematics and has some rather unique properties. The Cantor set was discovered in 1874 by Henry John Stephen Smith and introduced to the world by George Cantor in 1883. The Cantor set is a set of points lying on a single closed line segment, say from [0,1]. It is constructed as follows: Start with the closed interval Co-10.1]. Remove the open...
(6 pts) 3. Prove whether or not the set of ordered pairs of the form (w ) is a subspace of R'. (6 pts) 4. Prove whether or not the set of polynomials of the form a+Ox+ax is a subspace of P. 5. Let S = {(2,2,1,6),(1,3,5,1),(1,7,14,-3)} . (6 pts) Is S linearly independent or linearly dependent? (3 pts) b. Find (4 pts) 6. Give three examples of vectors in the span of {0.2.1),(3.1.0);
1. (15 points) Prove whether the following sets are linearly dependent or independent, and determine whether they form a basis of the vector space to which they belong. s 10110 -1 ) / -1 2) / 2 1 17 ) } in M2x2(R). "11-21 )'(1 1)'( 10 )'(2 –2 )S (b) {23 – X, 2x2 +4, -2x3 + 3x2 + 2x +6} in P3(R) (the set of polynomials of degree less than 3. (c) {æ4—23+5x2–8x+6, – x4+x2–5x2 +5x-3, x4+3x2 –...
Consider the construction of the Cantor set C c [0, 1] In the st step we remove the open interval (, ) ad are left with two closed intervals [0· and [릎,1]. Let J1 denote one of these two closed intervals. In the 2nd step, we divide J into three intervals and remove the open middle third interval. We are left with two closed intervals inside J. Let J2 denote one of these two intervals. For example, if Ji were...
Exercise 6.8. Recall the geometric description of the Cantor set. With Ko:-[0, 1], we constructed i Go(o) UG2(o). With d) the distance defined in (2), what is d(Ko,K1)? For any k e N, what is d(KkKo) and d(k,Kk+1)? (10 pts)
Exercise 6.8. Recall the geometric description of the Cantor set. With Ko:-[0, 1], we constructed i Go(o) UG2(o). With d) the distance defined in (2), what is d(Ko,K1)? For any k e N, what is d(KkKo) and d(k,Kk+1)? (10 pts)
4. (6 pt) Determine whether or not each set of vectors is a basis for R. Justify your answer you can determine the answer without calculation, say which basis property is guaranteed to fin and how you know that the property fails. (a) {(1,2,3), (4,5,6),(1,1,2),(-3,5,7)}. (b) {(0,2,5), (1,2,3), (0,3,4)}
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