可数集合

E^+ = {2,4,6,8,10,\ldots}

\mathbb{Z}^+ = {1,2,3,4,5,\ldots}

f(n) = 2n

\left| E^+ \right| = \left| \mathbb{Z}^+ \right>

\mathbb{Q^+} = \left{\frac{p}{q} \mid p \text{ and } q \text{ are positive integers} \right}

1from math import gcd
2from fractions import Fraction
3
4# Print for each reduced fraction x/y  on the diagonal numbered i-1
5def print_diagonal(num, i):
6    val = num
7    for k in range(i - 1, 0, -1):
8        if i%2 == 0:              # Traverse downward
9            a = Fraction(i - k, k)
10        else:                   # Traverse upward
11            a = Fraction(k, i - k)
12        if gcd(i - k, k) == 1:     # If the fraction is in reduced form
13            # The positive integer val+1 has image a 
14            val = val + 1
15            print(val, "-->",a)
16    return val
17
18
19print("Mapping from positive integers to rationals is as follows:")
20num = 0
21count = 10
22for i in range(2, count + 2):
23    print ("........ Diagonal Number ", i - 1, "........")
24    num = print_diagonal(num, i)