Go cut me a switch, boy, and I’ll show ya what ya get…
Which disciplines are those? Because I think I’d like to change my field of study . . .
English, philosophy, history, sociology, the whole slew of spinoffs of history and sociology called “<demographic identifier> studies”, political science, the more political end of economics, psychology…
Actually, even though there are right and wrong answers in most hard sciences, in practice it often doesn’t matter because if you lay your emphasis more squarely on the experimental end than the theoretical end it doesn’t matter. Formulate a hypothesis, test it, prove it wrong, publish. If I could publish results nobody had ever before proven wrong, I’d have had tenure years ago.
No, because if 0/0 was equal to anything including 0, I could still cancel it from both sides of your equation to make 6=3.
In case you object that I’m not allowed to cancel zeroes in 60=30 it is exactly because 0/0 is undefined (to cancel the zeroes I’d have to divide both sides by 0).
Precisely. As I previously posted, if 0/0 is defined to be any number, then you can show any number is equal to any other number. Can’t have that. So 0/0 is undefined. That’s the easiest explanation without getting into rings, fields, etc.
I think nivlac is correct, but to address dmartin, if you cancel the 0/0 from both sides, you’d simply get 0 again, and hence be stuck in an infinate loop, right?
Also, nivlac, since we can take that answer to point, what do you mean by "getting into rings, fields, etc. I’d like to know, so if you, or anyone else, don’t mind explaining this to me, be very nice.
WAIT!
You can’t just say 6(0/0) = 3(0/0),
if you do:
6x=3x
3x=0
x=0
then it seems to be ok…i mean consider this
6(2/2)=3(2/2) 6=3 obviously thats wrong, so you need to use variables first and foremost, before stating that if 0/0 equaled 1 or 0. IF that were true, you could use any number over itself to prove 6=3.
HOWEVER,
(6x/0) = (3x/0) for x=0 (assume 0/0 equals 1)
(60/0) = (30/0)
6=3 [obviously this is wrong]
now let’s try another situation,
(6x/0) = (3x/0) for x=0 (assume 0/0 equals 0)
(60/0) = (30/0)
0=0 [true!]
rebuttals anyone?
It’s the old truth–if you assume something false (0/0 = 1 in your case), you can prove any damn thing you like. That doesn’t mean what you’ve proved is true.
X/X=1
0/X=0
X/0=infinity
I say 0/0= all numbers from negative infinity to positive infinity, inclusive.
I say.
If you read the rest of the therad you will see what is meant by this.
To a mathematicvan ‘0’ is a generic term for the additve identity so we can only examine the quetsion by looking at general classes of objects that have an additive identity and some way of defining divison - a ring is probably the most general class of objet that has this, a field is a specifc type of ring (the integers are a ring, but not a field, whereas the rationals, the reals, the complex numbers are all fields).
The problem is that unless you say what your talking about (i.e. the rationals, reals, etc.) then we can only assume the most general case. Those who did not try to adress it terms of rings, etc, didn’t even say which matahematical object they were talking about; if you don’t specify what your talking about it’s impossible to prove anything.
2+2 = 5 implies 1 = 2 implies two are one. The Pope and I are two, hence the Pope and I are one, hence I am the Pope.
– Russell
Well, those who didn’t say rings generally quoted what they remember from calculus: “0/0 is indeterminate”, which is really shorthand (they’d forgotten) for “0/0 is an indeterminate form of a limit”. A perfectly understandable mistake, though a mistake nonetheless.