all finite set is countable.but,countable can be finite or infinite
A null set, a finite set, a countable infinite set and an uncountably infinite set.
Yes, finite numbers are always countable.
A finite set is a set that contains a limited or countable number of elements. For example, the set of natural numbers from 1 to 10 is a finite set because it has exactly ten elements. In contrast, an infinite set has no bounds and contains an uncountable number of elements, such as the set of all natural numbers. Finite sets can be characterized by their cardinality, which is a measure of the number of elements in the set.
Finite, no.
all finite set is countable.but,countable can be finite or infinite
A null set, a finite set, a countable infinite set and an uncountably infinite set.
Yes, finite numbers are always countable.
YES
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.
A finite set is a set that contains a limited or countable number of elements. For example, the set of natural numbers from 1 to 10 is a finite set because it has exactly ten elements. In contrast, an infinite set has no bounds and contains an uncountable number of elements, such as the set of all natural numbers. Finite sets can be characterized by their cardinality, which is a measure of the number of elements in the set.
here is the proof: http://planetmath.org/encyclopedia/ProductOfAFiniteNumberOfCountableSetsIsCountable.html
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.
the number of steps of an algorithm will be countable and finite.
prove that every subset of a finite set is a finite set?
Yes.
Finite, no.