Verified answer

Since it's false when b=0 and a > 0, I have to assume your definition of "naturals" is "positive integers" (there are two different definitions used in mathematics texts).

Under that assumption, note that

a | b

implies that there is some integer k such that

a*k = b.

Also, since a,b are positive, we can divide by a to solve for

k = b/a > 0.

In particular, this shows that k is positive, and the smallest positive integer is 1, so

1 ≤ k

Finally, multiply both sides of this inequality by a > 0 to find

a ≤ a*k = b.

Suppose that a|b.

So, b = ka for some positive integer k.

Finally, since k is no smaller than 1,

a = 1a ≤ ka = b, as required,

I hope this helps!

if not, then a > b.

Given a|b, then ak = b for some natural k.

a > b = ak

which gives you a false statement. I.e, 1 > k.

even if k = 1, 1 > 1 is still a false statement.