A strictly monotonic increasing sequence is bounded below, then we can conclude that

In mathematics, particularly in real analysis, a strictly monotonic increasing sequence refers to a sequence where each term is strictly greater than the preceding term. If such a sequence is bounded below, it implies that there exists a lower limit to the values in the sequence.

Conclusion

If a strictly monotonic increasing sequence is bounded below, we can conclude that this sequence will converge to its infimum (greatest lower bound). This is a result of the properties of monotonic sequences, particularly the Monotone Convergence Theorem, which states that a bounded monotonic sequence will always converge.

In simpler terms, since the sequence keeps increasing and cannot go below a certain value, it will approach a specific limit rather than continue infinitely or oscillate. Therefore, the conclusion is:

A strictly monotonic increasing sequence that is bounded below converges to its least upper bound ( supremum).