Everyone learns in primary school that you can't divide by zero, but few of us ever learn (or fully understand) why. The stock answer is that it gives you an answer of infinity. The truth is a bit more nuanced than that, and an old mechanical calculator offers the perfect illustration.
Try to divide a number by zero with a standard calculator, and you'll just get an error message. But as Eric Limer shows us over at *Popular Mechanics*, check out what happens when someone tries to do this on a Facit ESA-01 mechanical calculator, with the cover helpfully removed so all the internal workings are exposed:

The machine pretty much goes insane, its gears and cogs hammering away in a nonstop frenzy of clacking. WTF?

It has to do with how such machines work, and also with the nature of division — it's basically just "glorified subtraction", as the folks at Numberphile will tell you. To divide 20 by 4, the mechanical calculator perform a sequence of steps: 20 minus 4 is 16, 16 minus 4 is 12, 12 minus 4 is 8, 8 minus 4 is 4, and 4 minus 4 is 0. Voila! It takes five steps, so 20 divided by 4 equals 5.

But 20 divided by zero is just subtracting nothing from 20 over and over again. The calculator never arrives at an answer because it would take an infinite number of steps. And infinity is really more of a concept than an actual number.

As Limer explains: "The underlying cause for the freakout is that the poor machine is trying to hammer out an infinite sequence of commands, one by one. A computer will always do exactly what you tell it to do, even if that will take literally forever."

[Twisted Sifter via Popular Mechanics]

Credit: Numberphile/Flickr

## Comments

Does this mean the machine is INSANE

It means the machine thinks the world is flat because thats the limit of the folks who created it.

everything has a solution...even divide by zero.

if you divide x by three you interacted with x dividing it into three real parts. If you divide x by two you interacted with x dividing it into two parts. If you divide x by one you interacted with x dividing it into on part. If you divide x by zero you cease interacting with it...dividing it into no real parts.

Solution: X / 0 = NOT X (a set unrelated to X except at superposition). How is this useful? A string seperates one possibility from another. Point A. Point B. A string separates one possibility from another. A string forms during ongoing division (as opposed to a resolved division).

Spaceship divides the universe by zero (ceasing all interaction with the universe) and vanishes into NOT Universe...

Is 2/0 twice as much as 1/0?

:\

Isn't anything divided by zero, the original number, so three divided by zero equals three.???

No, you're thinking of any number divided by one.

Yeah but zero would be exactly the same thing. You're dividing by nothing so nothing changes.

Na say you got 10 apples and you give out apples to 0 people. How many apples does each person have?

It doesn't work there are no people to give anything too. So you can't say how many apples does no one have.

That's why typically then answer is called undefined, because there is no definec answer it just doesn't work.

If you have ten apples and you give them to no one, then you still have 10 left.

So you're saying:

3 / 1 = 3

3 / 0 = 3

Therefore 1=0

Yeah nah...

Yeah I know I'm wrong but I am right in a strange kind of way. Maths was never a strong point for me and shit like this always put me off it. You see, I can't get it out of my head that something divided by zero is zero. To my poor head, that doesn't make sense. When you divide by two, you regroup the number into two piles. Divide by three, you regroup into three piles. Divide by one and nothing changed...... And divide by zero, again nothing changes. It can't change as you're asking nothing to happen to the original group, just like dividing that group by one. Yes I'm wrong but common sense tells me it's right....... And hence I failed at maths at school. Stupid bloody numbers. Lol. And don't get me started on letters in maths. Letters are for words.

I empathise and was never much good at maths either.

One small correction, something divided by zero isn't zero, it's infinity.

Anything multiplied by zero = zero. Mainly because the reverse is true, that is nothing can't become something, it just becomes "more zero" which is still zero.

The way I understand the divide by zero problem is to remember that dividing by a fraction is the same as multiplying by it's reciprocal (Google explains this better than I can).

For example: 1 divided by 1/10 = 1 times 10 = 10

So extending this:

1 / a thousandth = a thousand

1 / a millionth = a million

etc

Then keep going until you have a fraction that's so small it's effectively zero. The reciprocal of that becomes so massively large that it's effectively infinity.

A good way to visualise this (I believe) is to imagine or graph the following:

3 / 3 = 1

3 / 2 = 1.5

3 / 1 = 3

3 / 0.5 = 6

3 / 0.1 = 30

etc.

3 / 0.001 = 3000

3 / 0 = infinIty

On a graph you can see that as the divisor gets smaller the answer is getting infinitely large.

Okay, that makes sense when you write it like that. Thank you

This is incorrect. If it was, then it will be possible to take the limit of the function and arrive at an answer. But there is no answer to x divided by 0.

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