More formally: given a positive integer n, the triple can be generated by the following two procedures:

For any positive integer n, the Euclidean space is connected and locally connected.

For every positive integer n, most groups of order n are solvable.

The positive integer n is the number of degrees of freedom.

For every prime number p and positive integer n, there exists a finite field with p elements.

Each positive integer n has 2 distinct compositions.

Then I tells us that for every positive integer n the statement S(n) is true.

"Given a positive integer n, find a nontrivial prime factor of n."

"Given a positive integer n, determine if n is prime."

For a positive integer n this takes the following form: