It would seem to be the case that if you have an equation in n variables, performing the same operation to each side of that equation provides an identical equation, in that if you graphed each equation in n dimensions you'd get the same graph.
Why is this, though? The first place I'd think to look would be the fundamental theorem of algebra, but I don't really see how that ties in here if it does at all.
Why is this, though? The first place I'd think to look would be the fundamental theorem of algebra, but I don't really see how that ties in here if it does at all.