When n tends to positive infinity, the limit of this sequence is e, that is, e = lim (1+1/n) n.

Some properties of number e make it especially convenient as the radix of logarithmic system. Logarithms based on e are called natural logarithms. It is represented by a mark ln that does not mark the bottom; Natural logarithm is often used in theoretical research.

In history, natural logarithm was mistakenly called Napier logarithm, which was named after the inventor of logarithm-Scottish mathematician J. Napier 16- 17. Napier himself has never had the concept of the base of logarithmic system, but his logarithm is equivalent to the logarithm whose base is close to 1/e, and Bilgi, his contemporaries, set a logarithm whose base is close to e.