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Q&A #3893

Teachers' Lounge Discussion: Dividing by zero

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From: Richard Askey <askey@math.wisc.edu>
To: Teacher2Teacher Public Discussion
Date: 2001012311:46:23
Subject: Re: Zero divided by zero (indeterminate form).

  About figuring out what 0/0 is, that is what differential
calculus is about.  Yes, it is necessary to understand this if
you want to really understand graphing, especially curves with
cusps.
  About n/0 when n is not zero, first ask the students what
a/b means when b is not zero.  Among other things, this is c
when b*c=a.  Then ask the students what number c gives
0*c=a?  Clearly, there is no such number, so n/0 is not
defined.  It is better to say it is not defined than to say it
is infinite.  When you get to graphing, and you graph y=1/x,
this graph is not defined when x=0, but becomes arbitrarily
large when x>0 goes to 0.
  Dick Askey


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