Which is exactly why we do not rely upon programmers to define math. Programmers set convenient tricks to make writing programs easier when dealing with special cases, like division by zero and infinities.
THESE DO NOT CORRESPOND TO THE REALITIES OF MATHEMATICS.
I could write a program that says 42/0 = apple, and you fuckers would think that made it true.
Division by zero is indeterminate, except in special cases. Infinity is not a number in the regular meaning of 'number.'
∞ ∉ ℝ
FAIL
Name:
Anonymous2006-05-07 5:57
everyone here fails for not knowing math beyond calc 1. a / 0 = ∞ on the Riemann sphere (i.e. CPL).
Name:
Anonymous2006-05-07 20:25 (sage)
>>175
"a / 0 = ∞ on the Riemann sphere"
which is a special case.
Name:
Anonymous2006-05-08 2:49
no, it's not.
Name:
Anonymous2006-05-10 17:07
>>25
(and all others)
There is no such thing as "division" in the zero ring (or the trivial ring)
Rings are not required to have the property that every element has a multiplicative inverse. Therefore division is not defined for rings.
Otherwise we're talking about groups but even then division isn't defined because multiplication in groups isn't necessarily commutative so there really isn't any definable division "operator".
So it requires a FIELD to have division, and fields require additive identity != multiplicative identity, which makes the trivial ring {0} usless.
So division by the additive identity is never possible. QED
Name:
Anonymous2006-05-10 18:54
a / 0 = ∞ in the zero ring, but not the Riemann sphere.
Name:
Anonymous2006-05-10 20:10
6 IS CONGRUENT TO 12 MOD 3
3 IS CONGRUENT TO 0 MOD 3
DIVIDE BOTH SIDES BY 0
2 IS CONGRUENT TO 6 MOD 1
Name:
Anonymous2008-06-29 4:10
On a graph, yes.
Name:
Anonymous2008-07-01 0:53
>>178
the zero ring {0} can be thought of as a field, where {0} is both the additive and multiplicative identity, and its own additive and multiplicative inverse, in which case 0/0 = 0.
although 0/0 is traditionally considered an indeterminant, it is colloquially treated as equal to 0 in most cases. similarly to how n/0 = \infty when n is nonzero, except in a few cases where paradoxes can occur which have to be specially dealt with.
>>184
But an infinite quantity of 0 can't fill 1. That's why it's more accurate to say it's UNDEFINED.
Name:
Anonymous2008-07-03 4:52
>>185
An infinite quantity of man-meat fills your sphincter every night.
Name:
Anonymous2008-07-03 5:54
Jeepers, that man-meat would be enough to propel semen to the speed of light, then.
Name:
Anonymous2008-07-03 9:03
1/0 is simply a line with no slope. It has always been defined as such in basic Algebra.
Name:
Anonymous2008-07-03 17:32
it's safe to say that the limit of 1/x as x approaches zero is infinity, but since infinity is just a concept there is no such thing as 1/0, since 1/0 is greater than infinity.
Name:
Anonymous2008-07-04 5:47
>>188
basic algebra defines a lot of shit out of convenience because actually explaining it would involve shit thats too complicated to comprehend for an 8th grader.
also, 1/0 is not a line, no matter what your graphing calculator wants to show you.
Name:
Anonymous2008-07-04 10:32
How is it not a line?
Name:
Anonymous2008-07-05 7:43
>>191
how CAN it be a line? its one number divided by another number... a line is a set of solutions to a linear equation.
Name:
Anonymous2008-07-06 12:27
er, X/0.
Name:
Anonymous2008-07-08 16:08
One thing:
0 is a number, a quantity. What you conclude of it is other thing. 'Nothing' isn't a Mathematical term.
>>196
That's a Danish/Norwegian slashed O, not the empty set. The empty set is ∅.
And yes, they are distinct.
>>197 Null set was once a common synonym for "empty set," but this usage should be avoided because "null set" is now a technical term in measure theory.