Hi all ! I am terribly sorry if this was answered before but i couldn't find the post. So that's the deal. We all know that while x→∞ (1+1/x)^x → e But I am deeply telling myself that 1/x goes to 0 while x goes to infinity. 1+0 = 1 and we have 1^∞ which is undefined. But also see that 1/x +1 is not a continuous function so i cannot simply take the limit of it and raise the value to x like : (limit of 1/x + 1)^x while x→∞ So can you please give me a rigorous proof for why this function approaches to Napier's constant ?