Final answer:
The set of all subsequential limits, S, is nonempty due to the Bolzano-Weierstrass Theorem in mathematics.
Step-by-step explanation:
In mathematics, we know that the set of all subsequential limits, denoted by S, is nonempty by a theorem called the Bolzano-Weierstrass Theorem. This theorem states that every bounded sequence in a Euclidean space has a convergent subsequence. The existence of a convergent subsequence implies that the set of subsequential limits is nonempty.
For example, let's consider the bounded sequence {1/n} where n is a positive integer. This sequence has subsequential limits of 0, which forms a nonempty set.
In summary, the Bolzano-Weierstrass Theorem ensures that S, the set of all subsequential limits, is always nonempty for bounded sequences.