Multiplication and Division
➌ Multiplication is repeated addition.
p + p + p = p·3
p·0 means 'adding p zero times', which is 0.
If we define p·(-q) as 'subtracting p q times', then integers are closed under multiplication too.
➍ Division is the inverse operation of multiplication.
p · q = r ┆ r / q = p ┆ r / p = q
If r is not a multiple of p or q, the result is not an integer.
By defining rational numbers as the ratios of integers, they become closed under division.
p · 0 = 0
0 / 0 is undefined.
0 / p = 0
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Multiplication and Division.
Multiplication is repeated addition.
p plus p plus p equals p times 3.
p times 0 means, adding p zero times, which is 0.
If we define p times negative q, as subtracting p, q times, then integers are closed under multiplication too.
Division is the inverse operation of multiplication.
p times q = r
r divided by q = p
r divided by p = q
If r is not a multiple of p or q, the result is not an integer.
By defining rational numbers as the ratios of integers, they become closed under division.
p times 0 = 0
0 divided by 0 is undefined.
0 divided by p = 0
