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No. The basic idea of proving why not is this:
1) The underlying space X is at least countably infinite (of course).
2) Use the properties of a sigma field (aka sigma algebra) to find a countable partition of the space, X = disjiont-union( X_i ).
3) Notice that the union(X_i, s in S) is in the sigma algebra for any subset S of natural numbers.
4) Notice that any union(X_i, s in S) is distinct.
5) Conclude, since the set of subsets of natural numbers is uncountable, so too is your sigma algebra.
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Is a whole number an finite set?
No, it is countably infinite.
What are kind of set?
There are finite sets, countably infinite sets and uncountably infinite sets.
What is the kinds of sets?
Closed sets and open sets, or finite and infinite sets.
What is infinite set in math?
An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite.
Is it possible to define a probability on a countably infinite sample space so that the outcomes are equally probable?
No, it is not.
What is an example of a countably infinite field?
c
The number of elements of a principal ideal domain can be?
The number of elements of a pid may be finite or countably infinite...or infinite also....but a finite field is always a pid
Is a whole number an finite set?
No, it is countably infinite.
What are kind of set?
There are finite sets, countably infinite sets and uncountably infinite sets.
Is the set of irrational numbers countably infinite?
No. The set of irrational numbers has the same cardinality as the set of real numbers, and so is uncountable.The set of rational numbers is countably infinite.
Are There are fewer rational numbers then irrational numbers?
Yes, there are countably infinite rationals but uncountably infinite irrationals.
What are the kinds of sets according to number of elements?
One possible classification is finite, countably infinite and uncountably infinite.
What do you mean by countably infinite and infinite?
Countably infinite means you can set up a one-to-one correspondence between the set in question and the set of natural numbers. It can be shown that no such relationship can be established between the set of real numbers and the natural numbers, thus the set of real numbers is not "countable", but it is infinite.
What is the kinds of sets?
Closed sets and open sets, or finite and infinite sets.
Is the set of all negative integers discrete?
Yes, because it is countably infinite.
What is infinite set in math?
An infinite set whose elements can be put into a one-to-one correspondence with the set of integers is said to be countably infinite; otherwise, it is called uncountably infinite.
Is intersection of two countably infinite sets can be finite?
Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.
