0 / 8 = 0

but how come 8 / 0 = error or E.......???

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- Jul 18th 2006, 01:56 PM #1

- Jul 18th 2006, 02:34 PM #2Originally Posted by
**sonymd23**

$\displaystyle \frac{16}{8}=2\text{ because }8+8=8\times2=16$

now try zero...

$\displaystyle \frac{8}{0}=\infty\text{ because }0+0+0+0....=0\times\infty\neq8$

so zero goes into eight infinite times, which we call undefined.

~ $\displaystyle Q\!u\!i\!c\!k$

- Jul 18th 2006, 02:36 PM #3

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Originally Posted by**sonymd23**

Why?

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1)**The embarassing physics answer**because when one number is divided into another number that says how many times a number goes into that number. For example, 4/2 = 2 because 2 goes in 2 times.

However, when you have 8/0 note that no matter how many times you add 0 you get thus thus you never reach 8 thus there is no such number.

2)**The improved applied mathematicians answer**because when we write 10/2=5 we mean that 2 times 5 is 10, by definition of what division is (opposite of multiplication). Now when you have 0/8 the answer is 0 because 0 times 8 is 0, good. But what about 8/0? We are trying to find a number such when mutiplied by 0 results in 8, but any number multiplied by 0 is 0 how can we ever get 8!!! Futhermore, then what is the answer to 0/0? Do we say it is any number cuz any number times zero is zero, according to this definition.

3)**The elegant and perfect pure mathematicians answer**I am not going to state it (I have before on this forum) because you would not understand so there would be no purpose. All, I can say when we limit divison for non-zero number we preserve a very important property called*divisors of zero*. Thus, to preserve this property we limit ourselves.

- Jul 19th 2006, 04:06 AM #4

- Jul 22nd 2006, 11:40 AM #5Originally Posted by
**sonymd23**

your question isn't meaningless at all - and very difficult to answer.

Let us assume that the division by zero is allowed. Then you can say that

$\displaystyle \frac{4}{4}=\frac{8}{8}=\frac{-1}{-1}=\frac{0}{0}=1$

$\displaystyle 5\ \cdot \ 0=0$. Divide both sides of the equation by zero and you'll get:

$\displaystyle \frac{5\ \cdot \ 0}{0}=\frac{0}{0}$. According to our assumption the result is:

5 * 1 = 1

So you see that numbers are ambiguous, if you allow the division by zero.

(One effect of this result is: You can buy the most expensive car for 1 $, because 245,456.99 $ or 1 $, it's the same)

Greetings

EB

- Jul 22nd 2006, 12:14 PM #6
## PH's second point

Originally Posted by**sonymd23**

$\displaystyle \frac{5}{0}=x$

multiply both sides by 0 $\displaystyle 5=x\times0$

solve: $\displaystyle 5=0$ as you can see this is incorrect. In fact the method to do this problem is incorrect because $\displaystyle \frac{0}{0}=\infty$

let's try it now, with this new information:

$\displaystyle \frac{5}{0}=x$

multiply both sides by 0 $\displaystyle \frac{5\times 0}{0}=x\times0$

extend: $\displaystyle 5\frac{0}{0}=0$

solve: $\displaystyle 5\infty=0$

this way doesn't work either! because 5 times infinity equals infinity, not zero. So as you can see, there is no mathematical way to express $\displaystyle \frac{x}{0}$

- Jul 22nd 2006, 05:56 PM #7

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- Jul 22nd 2006, 06:48 PM #8

- Jul 22nd 2006, 07:02 PM #9

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Originally Posted by**High School Teacher***real*reason why. But when I started doing formal math and seeing how the numbers and everything was constructed I finally understood and these things never bothered me ever since. For now put faith into mathematicians and try not to find what 0/0 is, because you will not. Same thing as saying, do not try to find $\displaystyle a/b=\sqrt{2}$ because you will not be able to. You might not know the reason but you place faith into the mathematicians and never try.

- Jul 22nd 2006, 07:09 PM #10

- Jul 22nd 2006, 09:36 PM #11

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