Any even or odd number can be written as one of 10x + 1, 10x + 3, 10x + 5, 10x + 7, 10x + 9, 10x + 0, 10x + 2, 10x + 4, 10x + 6, or 10x + 8, (x= 1, 2, 3,u2026.n); all 10x + 1, 10x + 3, 10x + 5, 10x + 7, 10x + 9, 10x + 0, 10x + 2, 10x + 4, 10x + 6, or 10x + 8, can be transferred in to 5 x 2y, y = 1, 2, 3, 4, 5, 6, 8,u2026m by repeating two arithmetic operation (3x + 1 and dividing 2). When y is an odd number, 3 times y plus 1 will always yield one even number, if the even number is not one of 2n, then the even number divide 2 once or more, a new odd number y’ will be yielded, but the new odd number must be different from the original y, 3 times y’ + 1 will yield another new even number, if the new even number is not one of 2n, then the new even number divide 2 once or more, a new odd number y’’ will be yielded, so on, every dividing operation will yield one new odd number which is different from previous odd number, every time 3 + 1 will yield a new even number which is different from previous even number, these operations can be going unlimited and infinite different even numbers will be yielded until reach one of 2n which is less than total even number, but is also infinite, that is: by an infinite number of repeating two arithmetic operation (3x + 1 and dividing 2), one of 2n must be reach, then 5 x 1 will be reach, final 1 will be reach, this statement must be true, then the Collatz’s conjecture will be the Collatz’s theorem