Re: Checking simplified algebraic expressions (the -3 test)

On May 4, 11:14=A0am, magi...@[EMAIL PROTECTED]
 (Arturo Magidin) wrote:
> In article
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> michalc...@[EMAIL PROTECTED]
 <michalc...@[EMAIL PROTECTED]
> wrote:
> >On May 3, 11:42=3DA0pm, Arturo Magidin <magi...@[EMAIL PROTECTED]
> wrote:
> >> > Solve you check by plugging the answers back in.
>
> >> > Factor you check by multiplying things back together.
>
> >> > Simplify... Well neither my students nor I were ever taught a
reliabl=
e
> >> > and simple check for simplified expressions. Example "Simplify (x^2
> >> > -1) / (x+1)" this becomes "x-1".
>
> >> And if "factor" you check by multiplying things back together, why is
> >> it that "simplify" cannot be checked similarly? You go from
(x^2-1)/(x
> >> +1) to x-1 by either long division (which can be checked through
> >> multiplication), or by factoring and cancelling; the factoring can be
> >> checked, and the cancelling can be checked simply by multiplying and
> >> dividing again. So how is this different from 'factor" and "solve"?
>
> You did not address this.
>
> >I always teach them that there are cases when this won't work and your
> >would need to test with all numbers to be sure. The remultiplying
> >before cancelling allwos them to check one step in a simplification
> >but not the whole process. You might be right that -2 would be a good
> >choice but I will have to think about it. As for the ad hominum attack
> >that I must think I am really clever for thinking of this,
>
> An "ad hominem" is a kind of fallacious argument. It is predicated on
> using the (lack of) qualities of the person advancing the argument in
> order to reject the argument being advanced. "Ad hominem" is not a
> synonym for "insult", in any case. And while I ->was<- making fun, I
> was not engaging in an ad hominem argument.
>

You are correct about what an ad hominum argument is and you did not
make an ad hominum argument. I said ad hominum attack, by which I
meant (perhaps somewhat unconventionally) you made a personal attack
against my character which i thought was unnecessarily hurtful.