RE: Dividing by zero
August 10, 2013 at 10:21 am
(This post was last modified: August 10, 2013 at 10:22 am by Whateverist.)
(August 10, 2013 at 7:18 am)ITChick Wrote: 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.)
