最接近欧拉 python 的 output

Question

how to find which formula is closer to euler

import math
n = abs(int(input("enter a number: ")))
e = math.e

first = (1+ 1/n)**n
second = (1- 1/n)**n 
if second == 1/e or second < 1/e:
    print("second is closest to e")
elif first == e or first < e:
    print("first is closest to e")
else:
    print("tie")

without programming

first = e = (1+1/n)^n

first = 2.7048138294215285

second = 1/e = (1 - 1/n)^n

second = 2.7319990264290284

so first is closer to Euler but my output always is give me second why?

forgot to mention n is 100

Answer 1

That is because your checks are not right. second is 0.3660323412732292 and 1/e is 0.36787944117144233 , so second < 1/e is in fact True but that doesn't mean that second is closer to e than first . Instead, you should compare actual distances:

dist_first = (first - e) ** 2
dist_second = (1 / second - e) ** 2

and then compare them:

if dist_first < dist_second:
    print("First is closer.")
elif dist_second < dist_first:
    print("Second is closer.")
else:
    print("Draw.")