is division repeated subtraction?

[michel paul]

This just struck me as important.

People are quick to assert that multiplication is repeated addition, and pointing out that it is not becomes a tricky discussion to have, but what about division as repeated subtraction? I think a lot of the same people might be quick to agree that no, division cannot be thought of as just repeated subtraction, and that's interesting.

Yes, you can think about division as repeated subtraction in order to compute certain quantities, but if you think about division only in that way it will be difficult to achieve the concept of ratio and rational number.

Something else has to happen to be able to see division as ratio.

For example ... slope!

Ratio is slope. How far up do you go in relation to how far forward you went?

--

​Michel

​

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"What I cannot create, I do not understand."

- Richard Feynman

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"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
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[Bradford Hansen-Smith]

Division is also multiplication. Divide the circle and get a multiple of parts. In folding the circle in half there is a ratio of one whole: two parts. The slop, in this case a curved path, goes from 180 degrees up to 90 degrees and down to 180 degrees.

Brad

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[John Mason]

Just as multiplication is NOT repeated addition, though repeated
addition is an instance of multiplication, so division is NOT repeated
subtraction, though repeated subtraction is an instance of division.

Multiplication at school is scaling (composition of fractions as
operators, scaling by real numbers); at university it is composition
(notice where mathematicians use juxtaposition or multiplication
notation: in group theory etc. and in functional analysis, powers series
and the like). I suppose this might make Division the undoing of
composition (at university) and the undoing of multiplication (at
school). But the undoing of scaling is itself scaling.

He said, rather assertively!

JohnM

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