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Multiplication is defined as repeated addition.
3x5 = 5+5+5
How do we define 10/2?
3x5 = 5+5+5
How do we define 10/2?
Originally posted by Hurkyl
Multiplication is generally defined as satisfying the particular axioms. When multiplying integers, it reduces to "repeated addition", but "repeated addition" doesn't extend to quantities like 3.7 * 4.1.
Division is generally defined as multiplication by a multiplicative inverse.
Originally posted by Doctor Luz
Repeated adition is not satisfied enven with negative integers.
Not sure here, but how can you define division when using the word INVERSE? INVERSE as in RECIPROCAL means DIVIDING into ONE.
It kind of does work.
Originally posted by Hurkyl
Definition: y is a multiplicative inverse of x iff y * x = x * y = 1
Compare with inverses of functions; a function g is a function of f if f.g = g.f = i (where i is the identity function and . means function composition)
Definition: for nonzero y, (x / y) is defined to be (x * z) where z is the unique multiplicative inverse of y.
That is how you define division using the word inverse.
Of course, from here, it's a trivial exercise from here to show that (1/x) is the multiplicative inverse of x.
And incidentally, you did not arrive at 3.7 * 4.1 with repeated addition; you added 3.7 a few times then used a distinct operation.
What about -1 * -1?