h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Not knowing the specifics of what you were talking about, and not wanting to complicate matters further, but in some number systems (C*) 1/0 is defined as infinity but not 1=0*inf...(see [Broken link removed by Moderator]Generally in C (which includes all subsets of C) 1/0 is not defined.

Just read what you wrote.

I personally find subtration and division too extreme because they are non-commutative, i.e. it makes a difference which way you put numbers around them, whereas with addition and multiplication this is not the case.

E.g.

1+2 =3 and 2+1 =3
2 x 3 =6 and 3 x 2 =6
However:
5-3 =2 whereas 3-5 =-2
6/2 =3 whereas 2/6 =1/3

Thus I think in a perfect world these two functions would not exist. Instead you would just multiply something by another number to the power minus one (one over that number) when you wanted to divide and use minus signs as well as plus when you wanted to subtract. I'll explain:

5 + (-3) =2 and (-3) + 5 =2
6 x 1/2 = 3 and 1/2 x 6 =3

That's probably in a different number system...in C* 1/inf=0 if memory serves me correctly, but 0*inf is not equal to 1 in this system. However we commonly work in R, the real number system. In this number system 1/inf is not defined.

Oops, the above is in response to SAS...the post didn't seem to go to the main post thingy...

And I've made another mistake...should have reread. 1/0=inf in C*.

** THIS IS JUST FOR FUN ** (but is interesting)
Well lets try to look at the problem x/0 in the real world:
A bookstore has a special offer.
You buy two books for $40, each book cost 40/2 = $20
(if you only buy one book it cost $25)
What if you don’t get any books but still pay $40 ?
What does each book then cost (for you)?
40/0 = ?

You don't get any books so they cost 0$ ?

You get...

annoyed

a telling-off (US=bawled out?) from your bank manager

laughed at in the street


Reminds me of the poster campaign for one of DNA's books - somewhere around 1990-93 when I worked in the local bookshop:

Douglas Adams' mum says 'buy 2 for the price of 3'! With picture of his mum (presumably). The sad thing is I got taken in by it, for a second.

rooftiler

"(see how annoying capping every first word is?)"


If we're being picky, so is the continual use of "presume" when you mean "assume"!

First I'd like to express how pleasantly surprised I am to have discovered a website where people get into conversations about calculus (I just joined H2G2 a few days ago). Where else can you find a group of people talking math and proving things in an online conversation like this? (Well, probably lots of other places, but that's beside the point!)

What I'd like to point out is that in calculus we have something very similar to 0/0: dy/dx. Basically, dy signifies a very, very small, infinitessimal change in the y direction, and dx is a very tiny change in the x direction. So dx is NOT zero, but it means "practically zero" or more accurately, "the limit as x approaches zero". So we have two things that are "practically zero" divided by one another, and we end up with something very important and significant: an instantaneous rate of change, which is essential to physics and much more. Similarly, when we take the integral of something, we are basically adding up a bunch of dx's a "practically infinite" number of times and getting some finite number. So it seems to me that the actual values of 0/0 and 0*inf. have much less significance than "practically zero"/"practically zero" and "practically zero" * "practically infinity".

I acknowledge that I'm not using much proper mathematical terminology in my explanation; part of that is because the way I understand all this best is to put it in physical terms, and part of it is because I am sure there will be people reading this who may not understand if it is too technical.

I have two problems with this:

Firstly, although mathematically we can make varuious statements about division by zero if it is attempted I do not think it reasonable to talk about the consequences of such an attempt being meaningfull - thus to draw analogies with x/0 etc seems a nonsense.

Secondly, the idea of "converging to infinity" is about as alien as I can imagine. How can anything converge with something not even remotely definable? If you can in fact demonstrate something that converges to infinity then you are realy saying that you can get to within any small distance of it ... in other words you have caught it by its non existant tail!

By dint of these two problems I feel that it is simply not worthwhile pursuing the 'algebra' presented.

For the person who asked, 0/0 does not equal 1. 0/0 is undefined, just like any other X/0... kinda thing. If it did, you could prove all sorts of crazy things, like 1=2.

A=B
2A=A+B Add A to each side
2A-B=A Subtract B from each side
2A-2B=A-B Subtract B again
2(A-B)=1(A-B) Simplify
2=1 Divide (a-b) on either side of the equasion to cancel it out.

Of course, you can't do the last step because you are dividing a-b, and since they are equal, you are dividing 0 by 0. So if 0/0=1, then 1=2.

Try sharing a cake between no people. You will be stood with a knife and a cake for eternity trying to achieve this.

The "sharing the cake" analogy for the division by zero reminds me of my love life at a certain point of the recent past :

If you have one cake, and two people want it, they have to share (1/2), and polyamory takes care of it,
If you have one cake, and only one person wants it, then its a monagamous couple (1/1),
But when I was the cake that nobody wanted (me/0), things looked very gloomy.

So their you go : division by 0 makes numbers very unhappy and depressed...


C.L.