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Dividing by Zero page 3

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Originally posted by Darkruler2005:

Calculators saying it is infinity (anyone really) are wrong, it cannot be any number, since multiplying zero with any number will not get it to any number except itself. To solve 5/0 = X, you will have to see what is X when you solve 0 * X = 5. This is impossible, not even infinity will make 0 reach any closer to 5.

It is undefined, or NaN (Not a Number), as you said.

you hurt my head

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For x > 0,
x/0 = undefined.
lim a→0- (x/a) = -infinity.
lim a→0+ (x/a) = infinity.
lim a→0 (x/a) = undefined.

For x < 0,
x/0 = undefined.
lim a→0- (x/a) = infinity.
lim a→0+ (x/a) = -infinity.
lim a→0 (x/a) = undefined.

For x = 0,
0/0 = undefined.
lim a→0- (0/a) = 0.
lim a→0+ (0/a) = 0.
lim a→0 (0/a) = 0.

lim a→0- (a/a) = 1.
lim a→0+ (a/a) = 1.
lim a→0 (a/a) = 1.

Think that’s about it. Anyone notice any I’ve missed?

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your hat

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this is the best answer to me;
first we assume that 1/0 has an answer.
we now write down 1/0 = X
in that case X * 0 = 1 .
because a number * 0 = 0, X has no answer.
now there are people who state that the answer is infinity.
this is not true.
we take an infinite row of 0s
if they should add up with a number > 0, at least one (probably more) of the infinite row of 0s should be > 0
however, if that is the case, that number does not belong in the row of 0s because when X > 0, X =! 0
so we kick that numbers out of our infinite row of perfect 0s.
because 0+0 = 0
and we can repeat this infinite times.
1/0 != infinity.
we now can safely conclude that 1/0 has no answer.
the same thing applies for every number that =! 0

for 0/0 the answer is a lot easier
if 0/0 = A
A * 0 = 0
Because every number multiplied by 0 becomes 0
A can be every number, being both real, imaginary, long, short or infinite.

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I do it on my spare time, silly gooses.

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My caculator broken oh no………

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Originally posted by CrystalShadow:

Actually, this equation DOES equal a paradox. As shown by a real life example.

I have 10 cookies. I want to divide the 10 cookies among my friends and myself. However, let’s remove those friends so that I’ve reduced the denominator closer to zero. I still have myself, which is 10/1. The only way to get to zero is to remove myself. 10/0. Now, if there are no receivers for the cookies to be divided among, then originally, no one possessed the cookies. The cookies may still exist, but they can be divided unto nothing, as nothing is there to distribute them. Therefore the amount of cookies is zero. Now our equation is X=0/0. Basic proportions indicate that 0/0 = 2/2 = 17/17, and so on. What’s any number divided by itself? One. But, if 0/0 =1, how so? If there are no cookies, and no one to claim them, how can the result be that each person gets a single cookie? They don’t materialize from thin air. Thus, this equation is nonexistent. However, if the equation is nonexistent, then this data has never been shown, which means that there’s still room for scientists to search the mystery of dividing by zero. Researching this can lead to the exact same result, and the loop is continuous. Paradox.

Now you people may proceed to discover loopholes and/or errors in my argument that I failed to notice.

I still want someone to try to find errors and/or loopholes because I’m sure this can’t be right, but I’m not sure how.

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Well, you’ve assumed that because x/x = 1 (for x != 0), then 0/0 = 1 too. This is not true. Can we not say by the same logic that because 0/x = 0 (for x != 0), then 0/0 = 0?

Clearly 0/0 cannot take two different values, simultaneously. Hence, it is undefined.

(If we take limits as well as equalites, it can also be argued that 0/0 = infinity and also -infinity too.)

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I never said that 0/0 actually equals 1, I just said that by basic logic, it should. However, since it can’t, it creates that paradox.

But I understand what you’re saying.

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Originally posted by CrystalShadow:

I never said that 0/0 actually equals 1, I just said that by basic logic, it should.

But by basic logic, it should also equal 0 ;-]

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Dividing anything by zero will have the result undefined, this does not change for 0/0. This is simply a rule, not really logical thinking.

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wow this topic is definitely a nerd attractor…

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Dividing by zero results in a phenomenon called “infinity”—a point at which all quantities are equal, so numbers lose all meaning.
The proof: n*0=0
whereas n=any possible numeric value

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Originally posted by PlainBlandMan:

What do you think will happen?

Then it will of been divided by zero!