Re: Gabriel's Theorem - what I have learned thus far.

From: N. Silver (mathelp_at_worldnet.att.net)
Date: 02/21/05 

Date: Mon, 21 Feb 2005 19:21:06 GMT

Jason wrote:

> Now why can't I have 0/0 = 1 ?

0/0 is what we might call an "undetermined form."
One way for you to see this is to understand that
when we divide 0 by 0, every quotient x checks.

               x
           -------
         0) 0
            - 0
            ----
              0

Another way for you to see this is to think of
proper fractions as percents of makes vs. attempts,
like when shooting free throws. 8/15 is possible.
So is 0/0. Who is 0/0? Someone who never shot a
free throw: fans in the stands; players on the bench;
players who were never fouled, etc. Their percentage
is undetermined.

> Gee, so much crap is mentioned on this forum...

You are a crap machine.

> and when I state something like this within the correct context,
> it gets shot down.

not within any correct context

> Does not x/x = 1 ?

if and only if x is not equal to 0.

> What prevents me from saying that 0/0 = 1 ?

Nothing! It's a free country, but you would be incorrect.

> If you have 0/0 mutiplied by some expression, it's perfectly
> valid to just drop it.

Only in your mathematically deranged mind.

> consider e^x * 0/0 = e^x. 0/0 must be 1 or
> else this would be untrue, no?

The left side is undefined.
Truth can come about from incorrect reasoning,
just as a falsehood can be derived from a false premise.
Suppose 0/0 = 1. We would have 0/0 + 0/0 = 1+1 = 2.
On the other hand, adding fractions, we would get:
0/0 + 0/0 = (0+0)/0 = 0/0 = 1. So, 2 = 1.

> In fact the only time an expression like this would be arithmetically
> incorrect is if 0/0 were multiplied by some constant value. But if we
> are looking at the product of 0/0 with an expression, it's perfectly
> valid. In fact this is exactly what you do when you derive e^x from
> first principles using the classic definition.

> Tst, tst, just a bit of lateral thinking wade - can't you apply your
> mind to this one? Think it over a few days and then maybe we can talk
> again. :-)

It's "tsk, tsk" not "tst, tst." And it's "demented thinking" not "lateral
thinking."

> Oh, please spend a few weeks providing some feedback on this posting:

> 1 - strongly agree
> 2 - agree
> 3 - dunno
> 4 - disagree
> 5 - strongly agree

minus infinity