Natural Numbers - is 0 a multiple of any natural number?

[aishvar...@gmail.com]

Let x and y be integers.  Then x is a multiple of y if there exists 
another integer z such that x = y*z.

That is the definition.  Now let x = zero and let y be an arbitrary 
integer.  Can we find an integer z such that 0 = y*z?  I think 
you'll see that choosing z = zero will do the trick every time.  So 
zero is a multiple of every integer.

Can someone please explain this? According to the above explanation, 5*0 = 0, 10*0 = 0, 12*0 = 0, etc. So 0 should be a multiple of any natural number. Please explain how if I'm wrong. Thank you.

[Himanshu Tripathi]

Dear,

I don't know why the professor has introduced 0 in the natural number, as far as I know, 0 is included in the whole number set. I have never studied about considering 0 in a natural number set.

So, 0 cannot be a multiple of any natural number.