I'm simply saying that 0 = 0 x a, where a is any number.I must have gotten you confused with Pete, because you where backing him up and this is what Pete has been saying. That is the whole point, if there is a factorization of zero, then the variable of the other factor will become meaningless. It will start to act like it is a zero itself. You will get equations where only zero could be a correct possible solution for that variable.

This is not controversial, it's very simple arithmetic. It's so simple that it's embarrassing to argue about it.

You wrongly insist that a must be 0, because you are confused over (slightly) higher mathematics, which leads to to get the basic stuff wrong.

As a rule of thumb, if your understanding of a topic you to an obviously wrong conclusion, then your understanding is incorrect.

Please demonstrate this assertion.So all I am saying is that if you factor out a zero and "a" is left as the other factor, you could end up with something like a + a = a.

And you haven't yet answered my last post.