Originally Posted by
tmthomp3
Proof of Reflexivity
suppose m is any integer
now m-m=0
but 3/0
since 0=3(0)
so 3/ (m-m)
hence by definition n of R, mRn
can anyone explain to me the logic behind following these steps to come up with this answer...per se...can anyone explain why the teacher subtracted (m-m) and made it the denominator int he aforementioned problem.
My guess is the following: perhaps the teacher defined R earlier by
mRn if m-n is divisible by 3.
Or "m is related to n by R if the difference m-n is divisible by 3"
"Reflexivity" means that every element is related by R with itself. (It's one of the properties of an equivalence relation). So to prove reflexivity, the teacher needs to prove that for any integer mRm, or in other words that
3 divides (m-m). But (m-m) is just zero, so 3 divides it in a kind of trivial way. So that's done.
I think the tricky bit here is that what the teacher is proving is so simple that it seems strange. But it's helpful to be very clear when you start to prove things, and check of everything precisely.