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Q: Does set of even counting numbers is well defined?

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Yes, except for one thing: mathematicians are not agreed whether 0 belongs to it.

Because the description which is given is sufficient to decide whether or not any given number is in the set.

Yes. Even numbers greater than 100 is a well defined set. (Although it is a set with an infinite number of members)

The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.

The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.

Yes it is. Given any number you can decide whether or not it belongs to the set.

Yes, they ARE.

yes

Prime numbers have only 2 factors and their set is not well defined because they do not follow an orderly mathematical pattern.

Any well-defined set of numbers.

Well, there is a clear definition, and at least in theory you can always determine whether a number is a primer number or not, so I would say, yes.

If there exists even one single item for which you cannot say whether it is in the set or not, the set is not well defined.

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