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 Discussion: All Topics Topic: Division by 0, Multiplication Related Item: http://mathforum.org/mathtools/tool/262/

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 Subject: Division by 0, Multiplication Author: tpowers Date: Jul 7 2004
I didn't like ths one as much as the Multiplication dialogue.  The dialogue does
not present a high-level discussion of why there is no "division by zero," nor
does it acknowledge that it is simplifying the whole story.  For example, it
says that there can be no "rope of length zero," but that is not even true;
e.g., a rope with length zero would just be defined as no rope.  This seems to
be in the same class of argument that leads one to believe that 0!, or 0^n have
no definitions.  In fact, a very natural definition of 1/0 is infinity, and many
kids will, indeed, ask why this is not the case.  The page does not even address
that question.  Also, the dialogue backs up the "no rope of length zero"
argument by saying there cannot be a particle of no mass, but that is actually
not even true (from the standpoint of modern physics).

Furthermore, the page does not discuss division as the inverse of
multiplication.  The lack of this bars the gate to algebra, and hence needs some
supplementary material.

Thirdly, there is no discussion of the relationship between fractions and
division, instead, they are defined implicitly as the same thing, and, with
regard to this, I can only say it is done without the least ceremony (to borrow
a phrase from George Berkeley).

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