Q: What is the symbol for a finite set?

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prove that every subset of a finite set is a finite set?

Finite, no.

all finite set is countable.but,countable can be finite or infinite

A finite set has a finite number of elements, an infinite set has infinitely many.

In mathematics, a finite set is a set that has a finite number of elements. For example, (2,4,6,8,10) is a finite set with five elements. The number of elements of a finite set is a natural number (non-negative integer), and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: (1,2,3,4, . . .)

An empty set is considered a finite set because it contains zero (0) elements and zero is a finite number.

An empty set (null set) is considered finite.

It is a set which contains a finite number of elements.

finite

A set which containing $and pi are the end blocks are the finite and without these are infinite

The empty set is a finite set.

The way I understand it, a finite set can not be an infinite set, because if it were an infinite set, then it would not be a finite set, and the original premise would be violated.