This is also a great example of the difference between '=' and '=='.
If the statement a = b, where to precede everything, then Sage would
know that a - b = 0, and would convert the statement 'a==b' to 'b==b',
which would frustrate the proof.

Jonathan

On May 23, 1:44 am, David Kirkby <david.kir...@onetel.net> wrote:
> On 21 May 2011 10:35, Juanlu001 <juanlu...@gmail.com> wrote:
>
> > Yesterday I was playing with symbolic expressions, and I had to apply
> > divide_both_sides(), and I encountered something funny: you can divide
> > by zero (with a bit of care). To show this, I've taken the classic
> > "proof" and created a worksheet:
>
> >http://flask.sagenb.org/home/pub/65/
>
> > Though I have got useful notices using other functions (such as "Is x
> > greater than zero?" when trying to solve an equation), I think that an
> > assumption should be made about the expression we are dividing by to
> > finally make the division.
>
> > Ideas?
>
> This reminds me of my school days. One of the guys in our chemistry
> class came up with a mathematical proof that proved humans did not
> exist. So we totally ignored him for the rest of the day! The
> cheamistry teacher asked why we was ignoring David B, so we told him
> that since David B had proved we did not exist, how would we be
> ignoring him.
>
> Dave

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