Give an example of a countable collection of finite sets whose union is not finite.

Q: If finite set A has a elements and finite set B has b elements, and a> b what is the minimum number…

A: Given that set A has a elements,  n(A)=a and set B has b elements,  n(B)=b with a>b .We have to…

Q: Write out in words the description of the set. {x\x € W, x < 9} The set of ---Select--- X, such that…

A: To write out in words the description of the set.

Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: Explain with an example of a topological space which is singleton that is open but not close and…

A: Example in refer of not  open but closed .Take , Here A is singletone set which is closed but not…

Q: Suppose we have a set A={1, 2, 3, 4, 5, 6}. What is the partition of A into three parts? Make sure…

A: We can partition of set A as below

Q: Is the Cantor set closed? Is it compact? Explain!

A:

Q: Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

Q: define sets.

A: A set is a collection of well defined objects.

Q: If the union of two sets is countable, then each set is also countable.

A:

Q: Prove that derived set of a bounded set is also bounded.

A:

Q: Prove that a nonempty set is bounded if and only if it is contained in a bounded interval

A: A non empty set S is called bounded if it has both upper and lower bounds, In a certain sense a non…

Q: Let A be a partially ordered set that has the least upper bound property. Then every nonempty subset…

A:

Q: Prove that a finite union and an arbitrary intersection of compact sets is a compact set.

A: Step 1: Step 2: Step 3: Step 4:

Q: a) Show that the least upper bound of a set of negative numbers cannot be positive. b) Show that the…

A: Given:-           a) Show that the least upper bound of a set of negative numbers cannot be…

Q: prove that the union of a countable set and an uncountable set is uncountable

A:

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: Give an example of an infinite number of open sets whose intersection is a single point

A:

Q: Prove that the set of all finite subsets of ω is countable. (Set theory)

A: The objective is to prove that the set of all finite subsets of ω is countable.

Q: (v) (E- A) specified using the most concise set builder notation without any word.

A: