[hijack]
Does all this stuff on infinities (not being able to divide them, etc.) mean you can’t simplify an equation where an infinity shows up? I thought scientists (physicists mostly) would occasionally work their equations so an infinity on one side cancelled out an inconvenient infinity on the other side. If you can’t divide them and so on how can they do this (or are they fudging)?
0 represents nothing. You may think that it is something because you see something, you see an 0…however, that is just a symbol for nothing.
However, I know most of you aren’t crazy about my answers, thus, I know that Microsoft must be pretty intelligent so I pulled out the Windows calculator, did 0/0 & got:
Result of Function is Undefined. Told ya.
If Bill Gates says it is so … I buy it. Dr. Iverson of IBM certainly isn’t in the same league. Sorry for the asking the question!
– DD
Hopefully one of the real math geeks will fill in the details, but I can get things started. The renormalization of infinities is indeed a necessary mathematical technique in physics. Particle physics and cosmology often come up with infinite quantities in their equations, and can’t really proceed along those lines unless they can cancel the infinities out, leaving only ‘normal’ numbers.
I don’t really know the technique, but it involves enumerating an infinite set so that it can be matched with another. For instance, you can match each member of {even positive integers} with a member of {odd negative integers}. Thus, you can say that they sort of share an ‘amount’ of infiniteness. So, these two sets could be operated on.
However, some sets are more infinite than others. You can’t assign each real number with a whole number, so the reals are ‘more infinite’ than the wholes. To cancel out an infinity of this order, you need to find something ‘equally infinite’ to balance it against.
So, there are strict rules about how you can do math with infinite sets. Just like other math, only a bit more arcane.
What’s this hijack? I’m only asking about 0/0, relative to real code problems … there are hundreds of theoretical infinity/zero/infinity/1/ … ?
Sorry for the hijack DrDoom. Arnold, in response to your question, posted some stuff on mathematical operations that are undefined (or indeterminiate). Totally unrelated to your OP I started asking questions about what Arnold had written.
Being that all of this stuff came about in this thread I started posting in this thread on an unrelated topic. Hardly the first time such things as this have happened on this board but I don’t blame you if you’re cheesed-off at the direction this is taking. If you prefer just say the word and I won’t continue on here and will start another thread on my spinoff.
Mathematically, zero divided by zero is undefined. The reasons why this is the case have been adequately discussed.
When dealing with computation devices, it is sometimes useful to alter the definition of division so that division by zero doesn’t generate an exception. There is no mathematical reason to favor any particular value when this is done; the value selected is arbitrary and should be driven not by mathematical reasons but by what is most useful in the application environment.
The only language I know of that systematically defines 0/0 is APL, where it is defined to be 1. (APL is weird.)
I believe that the 387 series of numerical accelerators can be told to disable floating exceptions, in which case 0/0 returns NaN (Not a Number), if I recall the specification correctly.
Hi Jeff_42 … just kidding … enjoy the sidebars … this thread is going no where anyways! Thanks.
– DD
Somebody complained of too much information on this issue, but I say the more the better. The trouble with any given book is it always oversimplifies things. The best thing about the internet is any given topic expands to infinity, at least potentially, with no control over respondents, which is the way it should be. I remember looking up some Japanese gods once and I found different added details in every book I looked at! In mathematics you never get the whole story. For instance, take the cyclic numbers. They are seldom even in mathematics dictionaries or encyclopedias and when they are in mathematics books they only epatiate on the cyclic numbers of the first order, ignoring all the other orders, if you can imagine that! In this case, even the internet doesn’t go into the other orders on these numbers anywhere except if a person already knows about them, he or she can extract the information from what IS in the wonderful AT&T Sloane’s number sequences, qui vide immediately.
I’m not a champion programmer, but the way I would code this is:
if mean1 = mean2 then t^2 = 0
else t^2 = formula above
Because (unfortunately) you need to provide for the case of division by zero.
For each case where you may have a division by zero, you have to have a condition handling the exceptions. That’s the only way to write solid programs AFAIK.
Or maybe you could change it to the set of all non-selfcontaining sets. Then your creditors would get hopelessly lost in a paradoxical maze.