What is the limit of (1-1/n)^n as n approaches infinity?

[intenzxboi]

Homework Statement

give the limit if it exist of (1-1/n)^n n=1 to infinity

the teacher wrote:
lim n goes to infinity (1+x/n)^n = e^x

so therefore
lim n goes to infinity (1-1/n)^n = e^-1

can someone explain this to me.

 

[intenzxboi]

how I'm i suppose to know that

(1+x/n)^n = e^x ??

 

[HallsofIvy]

how I'm i suppose to know that

(1+x/n)^n = e^x ??

What is your definition of "e"?