# Here's something strange

jz 22:53 23 Oct 2005
Locked

I was using the calculator that comes with Windows XP, and when I pressed 5 / 0 =, I got the message "cannot divide by zero". Is this a bug? What's the problem with dividing by 0?

DieSse 22:56 23 Oct 2005

Since the answer is infinity, it's hardly surprising the calculator refuses to do it!

Dan the Doctus 23:24 23 Oct 2005

Yup, ask yourself how many zeros there are in 5 - infinite, as DieSse says.

DieSse 23:59 23 Oct 2005

Strictly speaking, because infinity is not a number, it's a mathematical concept, then the calculator is perhaps more philosophically correct to say it can't be done.

Forum Editor 01:20 24 Oct 2005

Imagine filling a box with apples. The box can hold 100 apples. Now try filling it with apples that are half the size - you can get 200 of them in there. Now imagine a special magic apple that takes up no room at all. How many can you put in the box?

Many people think that numbers that are divided by 0 are 'infinite' but that's not correct; strictly speaking, such numbers should be referred to as 'undefined'.

That's why the calculator said what it did - and it was right.

Dan the Doctus 01:38 24 Oct 2005

TOPCAT® 15:21 24 Oct 2005

it is said that numbers can't lie. If so, then explain this!

Three guys decide to go fishing well away from home. They arrive at the venue and book in at a motel. At reception they find they can only have a room with three single beds, which they accept. The receptionist says it will be £10 each and this is paid over. The bell-boy takes their luggage up to the room and the guys follow.

On returning downstairs the receptionist then says to the bell-boy that, as it is now out-of-season, the guys have been overcharged and, taking out five pound coins tells the bell-hop to share them equally with the three guys. On his way upstairs he knows he can't share the coins equally, so he pockets two and gives the three men one each.

So each man has paid nine pounds for the room, which is £27, the bell-hop has taken two, which makes it £29, so where has that other pound gone? ;o) TC.

GroupFC 15:56 24 Oct 2005

They have been charged £8.33 each for the room, which the motel has received, although they have each paid an additional 67p each, which the bell-hop as stolen!

The moral of the story is never trust a bell-hop and definitely never tip them!!

Magic apples: it would certainly cut down on packaging and freight costs...

Wilham 20:12 24 Oct 2005

Someone is making fun of our ignorance.

GroupFC's explanation is still a penny out, which is not good arithmetic.

Truth is, of course, there is no sensible reason the £2 tip should be added to the £27, it is already part of that money and taking it away from £27 leaves the £25 downstairs.

On a higher level I don't like the answers to the 'infinity' problem. To Diesse I'd ask "Isn't a number itself a mathematical concept?".
To FE I'd ask how an apple, even a magic one, can stay as an apple when it reaches zero volume?

In truth, when calculations appear to produce division by zero, one has to step back an infinitessimal distance to see how the answer approaches infinity. There is a duality here with its reciprocal where a quantity approaches zero. It is at the core of infinitessimal calculus.

dukeboxhero 20:17 24 Oct 2005

just think of the cider you could make with magic apples

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