[Fsf-friends] [OT]Doing arithmetic with computers

Ramanraj K ramanraj.k@gmail.com
Wed Jun 8 08:32:24 IST 2005


On 6/7/05, Vivek Khurana <hiddenharmony@gmail.com> wrote:
> On 6/7/05, Ramanraj K <ramanraj.k@gmail.com> wrote:
> > While doing arithmetic, how is infinity represented on a computer?
> 
>  well use some arbitrary large number which is out of bounds from the
> current set being operated upon.

Joe Steeve wrote:
>There is no such thing as infinity in a computer. When a integer
>is divided by zero., the CPU will throw an exception.

Take the following equation:

sqrt{1 + 2 sqrt{1 + 3 sqrt{1 + 4 sqrt{1 + ...} } } }  = 3

Ramanujam proved the equation to be true. Please paste the above
equation into OpenOffice Math and it would be more clear.     In this
equation, we cannot use "some arbitrary large number" as Vivek
suggests and division by zero is not the only use for infinity.  (BTW
division by zero is assumed to be infinity and afaik there is no proof
for that).

There should be a way to represent ... or infinity in the above
equation on computers.  If there are no standard ways of doing it
then, we should devise a way to do it.  It is fairly important to be
able to represent infinity on computers just as easily as we represent
numbers, because it has many practical uses as well.  We may have to
define max and min values for variables, and sometimes it has to be
set at infinity.

If there are no standards for this, then:
[1] A special character could represent infinity (lemniscate :
sleeping 8 :) or three dots ...

AND/OR

[2] The last bit could be used to represent infinity.  If a n bit word
is used to represent integers, then the allowed integers have values
between -2^(n-1) and (2^(n-1)) - 1.  The maximum integer value could
be reserved to represent infinity

Whenever I had to represent infinity, I had used this notation:
Suppose for a variable x the max value is set to 3 and min value is
set to 0, then x could be any number between 0 and 3.  If max is set
to 0, and min is not 0, then it represents infinity,  x could
represent any value from min to infinity.  This works fine when min
would always be greater than 0, but if x would have to start from 0
then solution [1] or [2] becomes necessary.



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