1. **State the problem:** We need to find $n(A)$, the number of elements in the set $A = \{127, 128, 129, 130, \ldots, 141\}$. 2. **Recall the formula:** For a set of consecutive integers from $a$ to $b$, the number of elements is given by $$n = b - a + 1$$ 3. **Apply the formula:** Here, $a = 127$ and $b = 141$. So, $$n(A) = 141 - 127 + 1$$ 4. **Simplify:** $$n(A) = 14 + 1 = 15$$ 5. **Conclusion:** The set $A$ contains 15 elements.