The relation between set M = {x x = 2K + 1, K ∈ Z} and N = {y y = 4N ± 1, n ∈ Z}

The relation between set M = {x x = 2K + 1, K ∈ Z} and N = {y y = 4N ± 1, n ∈ Z}

K is an integer
Divided into odd and even numbers
K is odd, k = 2m-1, x = 2 (2m-1) + 1 = 4m-1, m ∈ Z
K is even, k = 2m, x = 2 * 2m + 1 = 4m + 1, m ∈ Z
So m = n