I read somewhere that division can be defined as multiplying the dividend by the multiplicative inverse of the divisor: a/b = a * 1/b, but the multiplicative inverse is another division problem.
In the forum (/viewtopic.php?id=19823), I was told that partitive division could be re-written as measurement division. How is that done? I want to know why is division the inverse operation of multiplication. Is there a more formal definition?
Thanks for help.
Real analysis starts with a set of definitions. You'll find these at
Axiom E in the first chapter requires the existence of multiplicative inverses.
ie. If a is a real number, then its inverse is 1/a such that
Which is why I have suggested that division is the inverse operation to multiplication.
In words, if there are b groups each containing c objects and a objects in total then the following are equivalent:
There is also this: