Are functions that are equal to a constant as you take a limit to infinty O(1)?

The below function converges to a constant as you take n to infinity.

$$f(n)=(1 + frac{1}{n})^n$$

$$lim limits_{n to infty}(1 + frac{1}{n})^n = e$$

Would this imply that it is O(1) since you can just upper bound it with a constant?