 Elementary algebra, in use for centuries and taught in secondary school, is the arithmetic of indefinite quantities or variables \(x, y,\ldots\). Whereas the definite sum \(3+4\) evaluates to the definite quantity 7, the indefinite sum \(x+y\) has no definite value, yet we can still say that it is always equal to \(y+x\), or to \(x^2 -y^2\) if and only if \(x\) is either \(-y\) or \(y+1\).