This thread is aimed particularly at @hoola  and @bangstrom   It took from the mid 1600s to the late 1800s to appreciate the full significance of this difference and even today it is rarely brought out in courses. When schoolboys move up from the algebra of values eg solve x+3 = 8  to the calculus they are introduced to 'functions'. But few, if any, are taught that functions have an algebra of their own. And this algebra is different (more complicated) from the very simp