Dividing by zero

[Tea Earl Grey Hot]

I'm not a math wiz. Why is it you can multiply by zero and get zero but you can't divide by zero?

Why doesn't 1/0 equal 0 but 1*0 does? Is there a reason or is it arbitrary?

[Silver]

In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary (real number) arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 has no defined value and is called an indeterminate form.

http://en.wikipedia.org/wiki/Division_by_zero

[Tea Earl Grey Hot]

In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary (real number) arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 has no defined value and is called an indeterminate form.

http://en.wikipedia.org/wiki/Division_by_zero

Yeah. I've seen that but it doesn't make sense to me. Why not say 1*0 is undefined and 1/0=0?

[Darth]

The "what is zero" thread has a video explaining it

http://atheistforums.org/thread-20325.html

[Captain Colostomy]

This was a good question for me too, TEGH. I'm so bad I have to drop trou(sers) just to count to 21.

[FallentoReason]

You can't divide by zero because it's an impossible "task". Say we want to divide 1 by 4.. well, all that means is that we're seeing how many times 4 fits into one. This is easy enough to do with the answer being one quarter. Now try your luck with 1/2. 1 divided by 1/2 (i.e. 0.5) is 2. 1 divided by 1/4 (i.e. 0.25) is 4. Let's go even smaller, say divide 1 by 1/100 (i.e. 0.01). That gives you 100. Well, by now you should see that the smaller you go (i.e. 1/2 => 1/4 => 1/100 etc etc) the bigger the answer. Why is this? Simply because what you're dividing by is so small that it fits lots and lots of times into (in this case) 1. So when you divide by *zero*, by nothing, zilch... well, how many times does *nothing* go into 1? It can't exactly be done, as you're adding 0 to 0 to 0... ...to 0 to 0 to get, well, 0 so far!

If you want to get real technical, the answer to 1/x approaches infinity as x approaches 0. As soon as you hit 0 though, the answer is undefined because it doesn't matter how many 0's you add, you'll never get to 1.

On a side note, in certain branches of philosophy, they've defined 1/0 as infinity, but that really bothers me as the heavy calculus stuff says otherwise!

[ITChick]

I'll try to explain it with salami sandwiches (simply because I am eating one now)

Let's say that I have four sandwiches and I want to share it between four people. (4/4). Easy. Each person gets one.

If I want to share it between two people (4/2), each person gets 2.

With one person, the lucky (maybe fat) person gets 4 (4/1)

Now I want to share it between 0 people. Uhm. Can't be done. The poor sandwiches will sit there uneaten forever. If I ask you how many sandwiches each person got, you will probably reply "which people!? There are no people!"

It gets even worse if I ask you: ok, how many sandwiches would each of these 0 people have to eat to ensure there are no more sandwiches left. You can't say 0, because then I still have the 4 stupid sandwiches.

This is different from multiplication. Let's say that I can make 10 sandwiches from one load of bread.

If I have two loaves I can make 20 sandwiches. (2x10)

If I have one loaf I can make 10 (1x10)

If I do not have any bread, I just can't make any sandwiches (1x0)

[Cyberman]

That was a great explanation; even I could understand it, and to me mathematics is like giving birth: it looks painful and messy, I'll never completely understand it and I'd rather leave it to people who seem to know what they're doing anyway. I've already dicked around in that whole area and that's the limit of my abilities.

Also: curses, beaten to the Numberphile card!

[Whateverist]

I'll try to explain it with salami sandwiches (simply because I am eating one now)

Let's say that I have four sandwiches and I want to share it between four people. (4/4). Easy. Each person gets one.

If I want to share it between two people (4/2), each person gets 2.

With one person, the lucky (maybe fat) person gets 4 (4/1)

Now I want to share it between 0 people. Uhm. Can't be done. The poor sandwiches will sit there uneaten forever. If I ask you how many sandwiches each person got, you will probably reply "which people!? There are no people!"

It gets even worse if I ask you: ok, how many sandwiches would each of these 0 people have to eat to ensure there are no more sandwiches left. You can't say 0, because then I still have the 4 stupid sandwiches.

This is different from multiplication. Let's say that I can make 10 sandwiches from one load of bread.

If I have two loaves I can make 20 sandwiches. (2x10)

If I have one loaf I can make 10 (1x10)

If I do not have any bread, I just can't make any sandwiches (1x0)

I like your method. I do something similar with my 8th graders. I announce I have $20 and intend to hand out $5 per student and ask how many will get the money. (Money makes everyone a genius.) I ask why not more and they correctly say the money will be gone after four people get theirs. I suggest handing out different amounts, they tell me how many get that amount and also keep telling me why no more do. When I get to $0 we can talk about how the money never runs out, how the original $20 is never touched and how this case is different than all the others.

Of course a more rote demonstration is to show that the answer to 20/5 is 4 and the test of that is that 4X5 = 20. Likewise 20/2 = 10 and it passes the test: 2X10 = 20. But if 20/0 = 0, then 0X0 would have to = 20. To say that the answer is infinity abuses the idea of infinity by treating it as a specific number, and anyway no very large number multiplied by zero will give you 20 (or 1 or any other number you care to divide by zero.)

[Cyberman]

Ow, my brain...