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No, a finite set can be a set of anything - as long as it has a finite number of members.
Some examples of finite sets are:
- the set of black Chess pieces in a chess set (16 members)
- the set of all red 2010 cars made by Ford (unknown but finite number of members)
- the set of planets orbiting our sun (8 members)
- the set of numbers between 14 and 23 that are integer multiples of pi (3 members) {5*pi, 6*pi, 7*pi} The elements of this set are all Irrational Numbers
- the set of marbles inside a pint jar (unknown but finite number of members)
- the set of Bowling balls in a 2 liter soda bottle (0 members as a bowling ball is too big to fit in a 2 liter soda bottle)
- etc.
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The set of all counting numbers less than one million is it finite or infinite?
Finite.
Is the set of whole numbers closed under subtraction?
It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.
The set of contains all the whole numbers and their opposites?
That is called the set of "integers".
Is the set of whole numbers are closed under multiplication?
If you can never, by multiplying two whole numbers, get anything but another whole number back as your answer, then, YES, the set of whole numbers must be closed under multiplication.
What is the cardinality of set b?
If set b is finite then the cardinality is the number of elements in it. If it is not finite then it depends on whether its elements can be put into 1-to-1 correspondence with the natural numbers (cardinality = Aleph Null) or with irrationals (Aleph-One).
