Equivilence relations, Reflexivity

Hi all,

I am given two relations and asked to prove which one is an equivilence relation for integers.

They are;

~ if is divisible by 5.

~ if is divisible by 4.

The problem i'm having is finding which one has reflexivity.

for example, which is not divisble by 5.

and, for all

So, is zero divisible by 4?

Re: Equivilence relations, Reflexivity

Think I've got,

zero divided by any integer is zero, but since zero is also an integer then it holds.

Am I right?

Re: Equivilence relations, Reflexivity

You are right. Zero is divisible by any nonzero integer.

Re: Equivilence relations, Reflexivity

Quote:

Originally Posted by

**Srengam** Think I've got,

zero divided by any **nonzero** integer is zero, but since zero is also an integer then it holds.

Am I right?

**That is correct.**