If division by zero produces a result of infinity, then
(1/0) = infinity.
If we multiply both sides by 6, we get
0 = infinity * 1
there you wouldn't multiply both sides by 1 you would mult both by zero.
expanding that you would get 0=1/infinity.
I believe that infinity and undefined are the same because infinity is undefined. And think about it,
when you divide a number by an ever decreasing decimal you would get an ever increasing number until your decimal becomes zero which would never happen because you could always add more zero's after the decimal ex:
.01, .001, .0001 , ... , .0000000000001 , ...
I guess that's why you can't divide by zero, because it almost doesn't exist.
in limits if you take the limit of 1/x as x-->infinity you would get zero. But if you just divide 1/x as x approaches infinity you would get an ever decreasing decimal because x never actually becomes infinity.
I think math is wierd. It's just amazing to think that people thought of a whole system from scratch to explain basically everything and it actually works.

just my 4 cents.