Coeff test

On 7/4/2014 5:30 AM, Rick Lyons wrote:


>
> OK.  I'm rather ignorant of number theory but
> I was thinking, "What's wrong, where's the danger,
> in dividing by zero?  Why am I not allowed to
> divide a number by zero?"
>
> If I divide three by zero I obtain:
>
>       3/0 = infinity       (1)
>
> If I divide five by zero I obtain:
>
>       5/0 = infinity       (2)
>
> Here's my question:  Does the "danger in
> dividing by zero" come from the fact that
> the 'infinity' in Eq. (1) does NOT equal the
> 'infinity' in Eq. (2)?
>
> Perhaps the danger is: we should NOT
> think of infinity as a number.
>
> [-Rick-]
>
Hi Rick,

To answer your first question, what happens if you multiply both sides 
of your equations (1) and (2) by zero?  If the multiplicative factor of 
zero is canceled by the zero in the denominator (works for any non-zero 
number), what you'll plausibly get is:

    3 = 0 * infinity     (1)
and
    5 = 0 * infinity     (2)

and so we conclude that 5 equals 3 (???)

In this case, the nonsense shows up immediately.  Unfortunately, we're 
not always so lucky;  hence the general advice "don't divide by zero".

Mike

Rick Lyons wrote:
> On Thu, 03 Jul 2014 16:53:04 -0400, robert bristow-johnson
<snip>
>
> Perhaps the danger is: we should NOT
> think of infinity as a number.
>

Right; I can't find the quote, but Euler thought of infinity as
simply a way - a method, if you like - to think about limits.

> [-Rick-]
>

-- 
Les Cargill

On 7/4/14 5:30 AM, Rick Lyons wrote:
> On Thu, 03 Jul 2014 16:53:04 -0400, robert bristow-johnson
> <rbj@audioimagination.com>  wrote:
>
>> On 7/3/14 4:28 PM, mnentwig wrote:
>>>> Yeah.  Can't tell you how many times I've seen software "proofs" fall
>>>> apart.
>>
>> well, if you have a finite number of cases in what you're trying to
>> prove, maybe one can test each one with a computer program.
>>
>> http://en.wikipedia.org/wiki/Computer-assisted_proof
>>
>>>
>>> Yes, analytic calculation seems more trustworthy...
>>>
>>> Let's start with
>>> A^2 - A^2 = A^2 - A^2
>>>
>>> On the LHS, factor out A.
>>> On the RHS, use A^2-B^2 = (A+B)(A-B)
>>>
>>> gives
>>>
>>
>> how do you get from here:
>>
>>> A(A-A) = (A+A)(A-A)
>>>
>>> thus
>>>
>>
>> ... to here?
>>
>>> A = A+A
>>>
>
> Hi Robert,
>    Markus' problem is actually kind of
> interesting.  It boils down to claiming:
>
>     P*0 = Q*0      ['*' mean multiply]
>
> which is a true statement.

it *is* a true statement for what it is.  but it does *not* mean that P 
equals Q.  it simply means that multiplying any number by zero results 
in the same result (which is zero)

> Then he divides both sides of the equation
> by zero.  But everyone correctly says,
> "It's illegal to divide by zero!"

"illegal" is in the mind of the holder.  so someone tells their computer 
to divide by zero, do the police come and put on handcuffs?

hell, it could've happened that 7*pi = 22 was "legal" in Indiana.

the issue is what is factual and what is not.

when we say that Q = N/D, we're simply stating that Q is such a number 
that when multiplied by D, the product is N.  the problem is, of course 
that if D=0, multiplying any Q by 0 does not get you a non-zero N.

multiplying by zero destroys information.  when you multiply P by some 
known non-zero "x", you know what P is from the product P*x.  but this 
is not the case if x=0.  if x=0, even if you know what x is, you cannot 
deduce what P is from knowing P*x (and x).

this is why dividing by 0 (whether it's illegal or not) cannot be used 
in a mathematical construction.  because dividing by D is undoing 
multiplication by D, but if D is 0, there is no undoing, the information 
of whatever D was multiplying is lost forever.


>
> OK.  I'm rather ignorant of number theory but
> I was thinking, "What's wrong, where's the danger,
> in dividing by zero?  Why am I not allowed to
> divide a number by zero?"
>
> If I divide three by zero I obtain:
>
>       3/0 = infinity       (1)
>
> If I divide five by zero I obtain:
>
>       5/0 = infinity       (2)
>
> Here's my question:  Does the "danger in
> dividing by zero" come from the fact that
> the 'infinity' in Eq. (1) does NOT equal the
> 'infinity' in Eq. (2)?
>
> Perhaps the danger is: we should NOT
> think of infinity as a number.

well, we can choose to think of infinity as a number or not.  but the 
reality is that it's not a number.  in that sense, "we should NOT think 
of infinity as a number".


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Sun, 06 Jul 2014 20:54:45 -0400, Michael Soyka <mssr953@gmail.com>
wrote:

>On 7/4/2014 5:30 AM, Rick Lyons wrote:
>
>
>>
>> OK.  I'm rather ignorant of number theory but
>> I was thinking, "What's wrong, where's the danger,
>> in dividing by zero?  Why am I not allowed to
>> divide a number by zero?"
>>
>> If I divide three by zero I obtain:
>>
>>       3/0 = infinity       (1)
>>
>> If I divide five by zero I obtain:
>>
>>       5/0 = infinity       (2)
>>
>> Here's my question:  Does the "danger in
>> dividing by zero" come from the fact that
>> the 'infinity' in Eq. (1) does NOT equal the
>> 'infinity' in Eq. (2)?
>>
>> Perhaps the danger is: we should NOT
>> think of infinity as a number.
>>
>> [-Rick-]
>>
>Hi Rick,
>
>To answer your first question, what happens if you multiply both sides 
>of your equations (1) and (2) by zero?  If the multiplicative factor of 
>zero is canceled by the zero in the denominator (works for any non-zero 
>number), what you'll plausibly get is:
>
>    3 = 0 * infinity     (1)
>and
>    5 = 0 * infinity     (2)
>
>and so we conclude that 5 equals 3 (???)
>
>In this case, the nonsense shows up immediately.  Unfortunately, we're 
>not always so lucky;  hence the general advice "don't divide by zero".
>
>Mike

Hi Mike,

    0 * infinity

Now there's an interesting concept!  Ha ha.

[-Rick-]