0/1

[bored_teen]

ever since we started learning division God knows when, i have been told that 0/1 cannot be done. but WHY? if we divide nothing by 1, wouldn't it just be nothing? but if we divided it by 2, wouldn't we have a lack of nothing? which is to say we'd have something? and if we divided 0 by 0, would we get infinity?

[bored_teen]

or if we divide 0 by 0, would we get All as opposed to Nothing? not infinity, per say, because infinity is an imaginary integer that includes all integers and itself as well, not to mention many more of itself. but All as in All? if we divide 0 by 0, we would essentialy be taking nothing from nothing, no times. so it would still be nothing. so if we take 0 divided by 1, instead of infinity, would we get All? All as in all. as in lions and tigers and bears.

[bored_teen]

i've just realised that i messed up on my concept of division. division isn't taking y out f x, y times. because if it was, 20/5 = -5. but it equals 4. division is separating x into y parts equally, then using 1 part as the answer. so 0/1 would be taking nothing, and separating it into 1 equal part. so you still have nothing. but if you take something out of nothing, because that is what 0/1 is doing, then you have a lack of nothing. i think i'm understanding why it can't be done. because it's too frustrating for anyone to figure out.

 

so can there be a negative infinity?

[the tree]

[math]\frac{0}{1}=0[/math] I don't know who told you otherwise.

 

Diving by zero however, is an invalid operation and there simply is no answer.

[cosine]

[math]\frac{0}{1}=0[/math] I don't know who told you otherwise.

 

Diving by zero however, is an invalid operation and there simply is no answer.

Excuse me for nitpicking, but there is a technical other consideration.

 

Any nonzero number divided by zero is undefined (unless working in some non-euclidean planes, then they are "the point at infinity"). As for [math]\frac{0}{0}[/math] is sometimes an exception if it is the limit of a function. If it is the limit of a function then it is called an indeterminate form and you need to use calculus to see if it has a value or not. (Cf: L'hopital's rule)

[bored_teen]

so 1/0 is the one we can't do? i would think that if you take nothing out of something, you would come up with the same amount of something... so it could equal 1. but then again, we are taking 1 and splitting it into no equal parts. so we have no parts. which means it's zero. so 1/0 = {0,1}

[Sisyphus]

No, it's neither 0 nor 1. It's not "taking out of" (that's subtraction). And you cannot divide something into nothing. The one can't just magically disappear.

 

You can, however, see what the answer approaches as the denominator approaches zero. Divide one by smaller and smaller numbers. One divided into a half is equal to two (Dividing one into a "half of a piece" means the whole must be two). One divided by a tenth is equal to ten. In other words, the smaller the denominator, the bigger the answer gets. As it approaches zero, the answer approaches infinity.

 

So isn't 1/0 just equal to infinity? No. First off, "infinity" is not a number. But more immediately, approaching is not the same as being equal to. For an example, approach zero from the other direction, i.e. smaller and smaller negative numbers. It approaches negative infinity.

[timo]

Division [math]a/b[/math] usually (and particularly in the case of the real numbers) means multiplication with the inverse, i.e. [math]a/b= a \, b^{-1} [/math] where the inverse [math]b^{-1}[/math] of [math]b[/math] is defined by [math] b \, b^{-1} = b^{-1} \, b = 1 [/math]. The inverse of 1 is 1 (proof: 1*1 = 1*1 = 1), 0 has no inverse (proof: [math] 0 \, x = x \, 0 = 0 \ \forall \, x \in R [/math]).

[bored_teen]

got it. leave the zeroes and ones to binary

[timo]

Not sure if you were serious, so I'll make my statement more explicit: 0/1 stands for [math] 0 \cdot 1^{-1} = 0 \cdot 1 = 0 [/math]. 0/0 doesn't stand for anything since [math] 0^{-1} [/math], the multiplicative inverse of 0, does not exist. It has nothing to do with binary: [math] 0/4 = 0 \cdot 4^{-1} = 0 \cdot 0.25 = 0 [/math].