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Explain or prove your answer. Is the following set finite, countable or uncountable? {(x, y) E...
From the class Introduction to Abstract Algebra on the section of countable and uncountable sets 3....
From the class Introduction to Abstract Algebra on the section
of countable and uncountable sets
3. Let X and Y be two nonempty finite sets. Let F(X, Y) denote the set of all function from X to Y. Is this set finite, countably infinite, or uncountable? Prove your answer
Problem 1. Let A C R be a countable set. Prove that R\ A is uncountable.
Problem 1. Let A C R be a countable set. Prove that R\ A is uncountable.
Question 7 Classify each of the following sets as finite, countable infinite, or uncountable (no proof...
Question 7 Classify each of the following sets as finite, countable infinite, or uncountable (no proof is necessary): A=0 B = {2 ER: 0 < x < 0.0001} C=0 D=N E = {R} F= {n EN:n <9000} G=Z/5Z H = P(N) I= {n €Z:n > 50 J=Z Bonus: Give an example of a set with larger cardinality then any of the above sets.
where Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.)...
where
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.) f(x)-sup f(x) | F is any finite subset of X TEF
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) 0} is a countable set. (HINT: Show that...
Let X be a set and let T be the family of subsets U of X such that X\U (the complement of U) is at most countable, together with the empty set. a) Prove that T is a topology for X. b) Describe the con...
Let X be a set and let T be the family of subsets U of X such
that X\U (the complement of U) is at most countable, together with
the empty set. a) Prove that T is a topology for X. b) Describe the
convergent sequences in X with respect to this topology. Prove that
if X is uncountable, then there is a subset S of X whose closure
contains points that are not limits of the sequences in S....
1. Determine whether each of these sets is countable or uncountable. For those that are countably...
please explain it step by step(
not use the example with number) thanks
1. Determine whether each of these sets is countable or uncountable. For those that are countably infinite, prove that the set is countably infinite. (a) integers not divisible by 3. (b) integers divisible by 5 but not 7 c: i.he mal ilullilbers with1 € lex"Juual reprtrainiatious" Du:"INǐ lli!", of all is. d) the real numbers with decimal representations of all 1s or 9s.
1. Determine whether each...
(iv) [ 12, 34] . Identify as finite, countable, or uncountable Os THE OF (vi) IBRATION...
(iv) [ 12, 34] . Identify as finite, countable, or uncountable Os THE OF (vi) IBRATION AL NUMBERS in IN TERVAL [ 142,314]. (vii) NUMBER BOOKS ON THE EARTH. (viii) NUMBER DIFFERENT RIGHT TRIANGLES (ix) P({1,2,3,..., 203) AL SEQUENCES TERMS BEING EITHER OR 1)s. Q) OF
2. Determine whether the given sets are countable or uncountable. Justify each answer with a bijection...
2. Determine whether the given sets are countable or uncountable. Justify each answer with a bijection (or table like we did with Q+) or using results from class/textbook. (a) {0, 1, 2} * N (b) A = {(x, y) : x2 + y2 = 1} (c) {0, 1} R Che set of all 2-element subsets of N (e) Real numbers with decimal representations consists of all 1s. (f) The set of all functions from {0,1} to N
a set (any set of objects) is said to be countable if it is either finite...
a set (any set of objects) is said to be countable if it is either finite or there is an enumeration (list) of the set. show that the following properties hold for arbitrary countable sets: a) All subsets of countable sets are countable b) any union of a pair of countable sets is countable c) all finite sets are countable
2. (Countable and uncountable sets and diagonalization) (a) A polynomial in variable x is an expression...
2. (Countable and uncountable sets and diagonalization) (a) A polynomial in variable x is an expression of the form c0 + c1x + c2x2 +c3x3 +· · ·+cdxd , where d is a non-negative integer and c0, · · · , cd are constants, called coefficients. Let P be the set of polynomials with integer coefficients. Show that P is countable.
From the class Introduction to Abstract Algebra on the section
of countable and uncountable sets
3. Let X and Y be two nonempty finite sets. Let F(X, Y) denote the set of all function from X to Y. Is this set finite, countably infinite, or uncountable? Prove your answer
Problem 1. Let A C R be a countable set. Prove that R\ A is uncountable.
Question 7 Classify each of the following sets as finite, countable infinite, or uncountable (no proof is necessary): A=0 B = {2 ER: 0 < x < 0.0001} C=0 D=N E = {R} F= {n EN:n <9000} G=Z/5Z H = P(N) I= {n €Z:n > 50 J=Z Bonus: Give an example of a set with larger cardinality then any of the above sets.
where
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.) f(x)-sup f(x) | F is any finite subset of X TEF
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) 0} is a countable set. (HINT: Show that...
Let X be a set and let T be the family of subsets U of X such
that X\U (the complement of U) is at most countable, together with
the empty set. a) Prove that T is a topology for X. b) Describe the
convergent sequences in X with respect to this topology. Prove that
if X is uncountable, then there is a subset S of X whose closure
contains points that are not limits of the sequences in S....
please explain it step by step(
not use the example with number) thanks
1. Determine whether each of these sets is countable or uncountable. For those that are countably infinite, prove that the set is countably infinite. (a) integers not divisible by 3. (b) integers divisible by 5 but not 7 c: i.he mal ilullilbers with1 € lex"Juual reprtrainiatious" Du:"INǐ lli!", of all is. d) the real numbers with decimal representations of all 1s or 9s.
1. Determine whether each...
(iv) [ 12, 34] . Identify as finite, countable, or uncountable Os THE OF (vi) IBRATION AL NUMBERS in IN TERVAL [ 142,314]. (vii) NUMBER BOOKS ON THE EARTH. (viii) NUMBER DIFFERENT RIGHT TRIANGLES (ix) P({1,2,3,..., 203) AL SEQUENCES TERMS BEING EITHER OR 1)s. Q) OF
2. Determine whether the given sets are countable or uncountable. Justify each answer with a bijection (or table like we did with Q+) or using results from class/textbook. (a) {0, 1, 2} * N (b) A = {(x, y) : x2 + y2 = 1} (c) {0, 1} R Che set of all 2-element subsets of N (e) Real numbers with decimal representations consists of all 1s. (f) The set of all functions from {0,1} to N
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