Is ZERO a multiple of any number?

• Sep 8th 2011, 01:56 PM
onemachine
Is ZERO a multiple of any number?
Is ZERO a multiple of any number?
• Sep 8th 2011, 02:05 PM
skeeter
Re: Is ZERO a multiple of any number?

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• Sep 8th 2011, 02:17 PM
TheBoss
Re: Is ZERO a multiple of any number?
I don't believe so.
• Sep 8th 2011, 02:22 PM
Plato
Re: Is ZERO a multiple of any number?
Quote:

Originally Posted by onemachine
Well, is it or is it not?

Quote:

Originally Posted by TheBoss
I don't believe so.

For all $\displaystyle x,~0\cdot x=0$ so the answer is YES.

But 0 is a divisor of no number.
• Sep 9th 2011, 03:39 AM
HallsofIvy
Re: Is ZERO a multiple of any number?
The usual definition of "x is a multiple of y" is "there exist an integer, n, such that x= ny". Since 0 is an integer, and 0 times any number is 0, 0 is a multiple of any number.

Some special circumstance add the requirement that n be a positive integer- in which case the answer would be "no". However, those "special circumstances" typically are that we are only working with positive integers so the question would not arise so I will still say "yes, 0 is a multiple of any number."
• Sep 9th 2011, 03:40 AM
HallsofIvy
Re: Is ZERO a multiple of any number?
Quote:

Originally Posted by TheBoss
I don't believe so.

Would you like to expand on that? Why don't you believe so?
• Sep 9th 2011, 04:54 AM
CaptainBlack
Re: Is ZERO a multiple of any number?
Quote:

Originally Posted by TheBoss
I don't believe so.

What you believe is irrelevant, it is or is not in consequence of the definitions of the terms etc.

So don't tell us what you believe, explain why or why not in terms of the relevant concepts.

CB