The number of stars is finite.
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Pi is an irrational number. As such, it has an infinite number of digits.
A finite set is one containing a finite number of distinct elements. The elements can be put into a 1-to-1 relationship with a proper subset of counting numbers. An infinite set is one which contains an infinite number of elements.
No. Each integer is finite. There is an infinite number of them though.
No, it is countably infinite.
The set of integers is an infinite set as there are an infinite number of integers.