I’ve begun to study math on my own. I’m at the bottom. I did a question finding multiples and got them all wrong because I didn’t include zero.
You are watching: Is 0 a multiple of every number
What is your definition of "multiple"?
The standard is:
B is multiple of A if exists N integer such that B=NA.
0 is multiple of A for every A because if we choose N=0 we have 0=0 x A =0
Exactly. By the way, we use this definition because it means that facts like
an integer is odd if it is one more than a multiple of 2
in decimal any Integer ending in "0" is a multiple of 10
the sum of two multiples of 5 is a multiple of 5
sin(x) = 0 of and only if x is a multiple of π
are easier to write than if we had to say "multiple... or zero."
Granted, there are some cases where we want to exclude 0, and our definition means we then have to say "nonzero multiple," but this is less common that the cases where it is good to include 0.
Yes, it is, 5*0 = 0, N*0 = 0
A multiple is commonly defined as, y is a multiple of x if kx=y, where k is some integer. We see that if k=0, x can be any number and y will be 0.
We can use some examples. 0*5=0, so 0 is a multiple of 5. According to https://www.mathsisfun.com, x doesn't even need to be an integer so 0 would also be a multiple of pi.
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