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Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
Show that the union of two countable sets is countable?
CHECK THIS OUT http://www.mathstat.dal.ca/~hill/2112/assn7sol.pdf
Is the set of all irrational number countable?
No, it is uncountable. The set of real numbers is uncountable and the set of rational numbers is countable, since the set of real numbers is simply the union of both, it follows that the set of irrational numbers must also be uncountable. (The union of two countable sets is countable.)
What is the cardinality of a union of two infinite sets?
The cardinality of finite sets are the number of elements included in them however, union of infinite sets can be different as it includes the matching of two different sets one by one and finding a solution by matching the same amount of elements in those sets.
What is a mathematical process in which sets are combined?
The union of two sets.The union of two sets.The union of two sets.The union of two sets.
Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
Is something that is finite always countable?
Yes, finite numbers are always countable.
Show that the union of two countable sets is countable?
CHECK THIS OUT http://www.mathstat.dal.ca/~hill/2112/assn7sol.pdf
What is the Difference between a finite set and countable set?
all finite set is countable.but,countable can be finite or infinite
Is the set of all irrational number countable?
No, it is uncountable. The set of real numbers is uncountable and the set of rational numbers is countable, since the set of real numbers is simply the union of both, it follows that the set of irrational numbers must also be uncountable. (The union of two countable sets is countable.)
Is counting measure indeed a measure and is this always sigma-finite?
It is a measure, but it isn't always sigma-finite. Take your space X = [0,1], and u = counting measure if u(E) < infinity, then E is a finite set, but there is no way to cover the uncountable set [0,1] by a countable collection of finite sets.
What is the cardinality of a union of two infinite sets?
The cardinality of finite sets are the number of elements included in them however, union of infinite sets can be different as it includes the matching of two different sets one by one and finding a solution by matching the same amount of elements in those sets.
What are finite sets?
They are sets with a finite number of elements. For example the days of the week, or the 12 months of the year. Modular arithmetic is based on finite sets.
How prove that the set of irrational numbers are uncountable?
Proof By Contradiction:Claim: R\Q = Set of irrationals is countable.Then R = Q union (R\Q)Since Q is countable, and R\Q is countable (by claim), R is countable because the union of countable sets is countable.But this is a contradiction since R is uncountable (Cantor's Diagonal Argument).Thus, R\Q is uncountable.
What is the kinds of sets?
Closed sets and open sets, or finite and infinite sets.
What are steps of algorithm?
the number of steps of an algorithm will be countable and finite.
Give you examples of finite sets of numbers?
sets
