In a numeric, non-empty, finite set the elements can be arranged in order. If this order is represented by:
{e0, e1, e2, ...,en} where ei≥ei-1 for i>0.
en is the upper bound, U, and en≥en-1, en-1≤U.
In an infinite series the infinite set consisting of individual terms (ai) of the series, such that all ai>ai-1 for 1<i≤n, then an>an-1 as n→∞, the series converges to an upper limit U. No element of the series exceeds U. (Many series converge to a limit, but the terms alternate from above to below that limit. These series would not then be bounded above because of the bidirectional approach to the limit. In this question, because the series or set is bounded above, no individual element in the set can exceed the upper bound.)