Is Zero Divisible by Zero and Four?

[cragar]

Homework Statement

determine which are true and false.
4|0 and 0|0

Homework Equations

a is divisble by b provided there is an integer c such that

bc=a

The Attempt at a Solution

on the first one 4|0
4x=0 , 0 would work for this.
and 0x=0 any integer would work for this but I am worried about division by zero
or something weird with zero , maybe I am overlooking this.

 

[HallsofIvy]

No, 0 does not divide 0. You definition
"a is divisible by b provided there is an integer c such that bc=a"
is not completely correct. It should be
"a is divisible by b provided there is a unique integer c such that bc=a"

 

[cragar]

I wrote it how my book wrote it. Thanks for your response by the way . So meaning there is only one integer c such that bc=a

 

[BloodyFrozen]

I wrote it how my book wrote it. Thanks for your response by the way . So meaning there is only one integer c such that bc=a

Yep, I think so. What are numbers are there such that 4x=0?

 

[cragar]

so x=0

 

[BloodyFrozen]

so x=0

Yes, like HallsofIvy said (one unique solution)

 

[cragar]

ok , thanks , just making sure.