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

[V. Sasi Kumar]

On Wed, 2005-06-08 at 08:32 +0530, Ramanraj K wrote:
> (BTW division by zero is assumed to be infinity and afaik there is no proof
> for that).

If I remember my math, division by zero is properly said to be
indeterminate, and not infinity. Infinity is not a number, but a concept
-- if that does make sense.

> 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

I am a little confused. Are you talking of writing infinity? In that
case, the infinity character is available. But when you want to do
actual computation, you cannot obviously do an iteration an infinite
number of times. So there we are forced to select an appropriately large
number that could stand for infinity.

It may be interesting to know that there are different kinds of
infinity. For instance, there are an infinite number of integers. But
there are an infinite number of rational numbers between any two
integers. So these two infinities cannot be considered to be of the same
kind. If I remember right, they are represented by the Hebrew alphabet
aleph. So we have aleph1, aleph2 and so on.

Best
V. Sasi Kumar