Message Forum: Re: Dividing by zero

Re: Dividing by zero

Posted By: Matthew, on host 62.30.192.1
Date: Sunday, December 30, 2001, at 07:02:37
In Reply To: Re: Dividing by zero posted by Silon on Sunday, December 30, 2001, at 05:14:59:

> Look at it this way: 0 can go into 0 0 times, thus 0 divided by 0 = 0. Zero can also go into 0 1 time, thus 0 divided by 0 = 1. It will also work with 2, 3, 4, 5, and up to infinity.
>

Which is exactly why 0/0 is undefined. It's not "anything you want it to be," because mathematical functions should never include choice. Mathematically,

lim x/x = 1
x->0

and

lim 2x/x = 2
x->0

so there are two functions that tend toward 0/0, but their values are different. The idea of getting progressively closer and closer to evaluating 0/0 is used in Calculus (the tangent idea of differentiation), but 0/0 is never actually evaluated itself.

Matthew

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Message:	> > Look at it this way: 0 can go into 0 0 times, thus 0 divided by 0 = 0. Zero can also go into 0 1 time, thus 0 divided by 0 = 1. It will also work with 2, 3, 4, 5, and up to infinity. > > > > Which is exactly why 0/0 is undefined. It's not "anything you want it to be," because mathematical functions should never include choice. Mathematically, > > lim x/x = 1 > x->0 > > and > > lim 2x/x = 2 > x->0 > > so there are two functions that tend toward 0/0, but their values are different. The idea of getting progressively closer and closer to evaluating 0/0 is used in Calculus (the tangent idea of differentiation), but 0/0 is never actually evaluated itself. > > Matthew
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