A subset of some set X is, by definition, any set whose elements are entirely contained in X. So the answer is yes. As an example, take your infinite set, and select 3 or 10 or any finite number of your favorite elements in this set. The set of your chosen elements is a finite subset of the infinite set.
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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.
Sets are collection of distinct objects. In mathematics there are different types of sets like Finite set, Infinite set, Universal set, subset, equal set, equivalent set. Example of Finite set {1,2,3,4}. Infinite set:{1,2,3....}.
A proper subset is a subset that includes some BUT NOT ALL of the elements of the original set. If the subset is finite, its order must be smaller than that of the original set but that need not be the case if the two sets are infinite. For example, even integers are a proper subset of all integers but they both contain an infinite umber of elements.
A set which containing $and pi are the end blocks are the finite and without these are infinite
If a set has "n" elements, then it will have 2n subsets. This number of subsets is always larger than the number of elements - whether the set is finite or infinite.