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Re: apples and oranges



I agree with Bob.
For pure dimensionless numbers --> 4*3=4*(1+1+1)=4+4+4
Now suppose I multiply 4N by 3m. In that case:

(4N)*(3m)=4*N*3*m=4*N*m*(1+1+1)=(4+4+4) Nm

This illustrates "that multiplication is a shorthand for repetitive
addition", even when numbers represent physical values.
Where do we "add apples and oranges"? Where is the danger
of adding Newtons to meters? It was a nice verbal trap for me;
thanks Ed.

I was wrong in writing: "In cases like this multiplication is no
longer a shorthand for repetitive addition, as it is when one of
the multipliers (or both) is a pure number."
Ludwik Kowalski

Bob Sciamanda wrote:

When I multiply x times y I am adding y to itself x times, so
I am adding together only things of the same kind.