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What is the Difference between a finite set and countable set?
all finite set is countable.but,countable can be finite or infinite
What are the different types a of set?
A null set, a finite set, a countable infinite set and an uncountably infinite set.
Is something that is finite always countable?
Yes, finite numbers are always countable.
Is a set of prime numbers an finite set?
Finite, no.
Why is an empty set a finite set?
An empty set is considered a finite set because it contains zero (0) elements and zero is a finite number.
What is the Difference between a finite set and countable set?
all finite set is countable.but,countable can be finite or infinite
What are the different types a of set?
A null set, a finite set, a countable infinite set and an uncountably infinite set.
Is something that is finite always countable?
Yes, finite numbers are always countable.
Is the union of finite countable sets finite?
YES
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.
Prove that a finite cartesian product of countable sets is countable?
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
Is every subset of a finite set is a finite?
prove that every subset of a finite set is a finite set?
What are steps of algorithm?
the number of steps of an algorithm will be countable and finite.
Can set of rational numbers forms a borel set?
Yes. the set of rational numbers is a countable set which can be generated from repeatedly taking countable union, countable intersection and countable complement, etc. Therefore, it is a Borel Set.
Is every subset of a countable set is countable?
Yes.
Is a set of prime numbers an finite set?
Finite, no.
What the differentiate between finite set and infinite set?
A finite set has a finite number of elements, an infinite set has infinitely many.
