how do i show, a is an integer

1) a|0?
2)0|a?

Question

how do i show, a is an integer 

1) a|0?
2)0|a?

zzr0ck3r · Answer

does 0 divide anything?

anonymous · Answer

no.

zzr0ck3r · Answer

but I don't see how either show a is an integer, maybe i'm missing something.

anonymous · Answer

a is an integer is a condition. i just need to prove it or sth. my textbook is very subtle about requiring wat form of proof.

zzr0ck3r · Answer

a is an integer if it can be generated by <1>

zzr0ck3r · Answer

you are saying a is an integer and you need to prove a|0 and 0|a?

anonymous · Answer

yeah. or show, as the textbook puts it.

zzr0ck3r · Answer

well part 1 makes no sense because 0 is in integer and 0 does not divide 0, and the second part makes no sense because nothing divides 0. So you can't prove either.

anonymous · Answer

ah well. thanks anyway.

zzr0ck3r · Answer

is this exactly as the book shows the question?

anonymous · Answer

yeah.

zzr0ck3r · Answer

you can say, if a is an integer and a is not 0, then 0=K*a when k=0, so a|0 because k is an integer (by definition of a|b), for part two nothing divides 0 is your counterexample:)

anonymous · Answer

wow. right. thanks.