Math Is Fun Forum

atran

Member

Registered: 2013-07-12

Posts: 91

What's the formal definition of division?

Hi;

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: What's the formal definition of division?

hi atran,

Real analysis starts with a set of definitions.  You'll find these at

http://ramanujan.math.trinity.edu/wtren … ALYSIS.PDF

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

So if

Which is why I have suggested that division is the inverse operation to multiplication.

If

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:

http://www.wolframalpha.com/input/?i=de … f+division

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob