the problem with this is the first assumption is only true with values of x=0
ie the first assumption is a solve-able equation with only one possible value of x.
you cannot get a 0 on one side of an equation and start multiplying & dividing. i forget the name of the rule that says you cannot do this... anyone?
that's part of an axiom for fields. ...the inverse axiom for the "*" operation (which may or may not be multiplication over R): "for all elements c in field F except for 0, there exists an inverse element d such that c*d = e, where e is the identity element."
we exclude 0 from this rule because if it had an inverse, 1 would be the same number as 0, which would cause every element in the field to also be 0!
should be in any linear algebra textbook.
oh, and i think the guy was joking, mac.
