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

Pubkeybreaker <pubkeybreaker@[EMAIL PROTECTED]
> wrote:
>On May 15, 9:09 am, Fatal <fa...@[EMAIL PROTECTED]
> wrote:
>>Pubkeybreaker a écrit :
>>>
>>> And this expression does NOT equal x-1 everywhere.
>>
>> You're wrong, it is equal to x-1 in the polynomial world.
> 
> (1) The expression 'polynomial world' is mathematical gibberish.

Nonsense, I've heard similar such remarks made by many 
esteemed mathematicians when speaking informally.

> (2) If we are working in the polynomial ring Z[x], 
> the problem needs to STATE that.  

But your post doesn't include any context stating that 
the expressions denote polynomial _functions_ either. 

> Otherwise, the default assumption in elementary high school
> algebra is that all manipulations take place over R.

Nowhere in your post (that we replied to) is there any remark
implying that problem is in the context of high-school algebra. 
Going all the way back to the original post I see that the
o.p. is tutoring 8th and 9th graders. However, you snipped that
context from your reply, so you shouldn't be surprised to get 
more general replies like ours after such sloppy editing.

> Please tell us where you got your math PhD. Or even your
> undergraduate math degree.

Stop bullying students - it is quite cowardly. If you must
pick fights then at least challenge someone at your own level.

>> In the world of fractions of polynomials, however, 
>> "simplest" has a sense (simplest elements form of fractions).
> 
> There is no canonical mathematical definition of the word 'simplest'.

There certainly is in the context of his statement
and, more generally, for fractions over gcd domains
(with sufficiently canonical properties).

> And 'world of fractions" is mathematical gibberish.

Any competent mathematician can rigorously interpret
that phrase in the context of his statement. Again, such
a remark might indeed be made informally by a professor.
 
> In short, you have no idea what you are talking about.

Do you?  Have you stopped beating your students?

--Bill Dubuque