# Math Help - meanless question

1. ## meanless question

0 / 8 = 0

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

2. Originally Posted by sonymd23
0 / 8 = 0

but how come 8 / 0 = error or E.......???
Let's do an example...
$\frac{16}{8}=2\text{ because }8+8=8\times2=16$

now try zero...

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

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

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

3. Originally Posted by sonymd23
0 / 8 = 0

but how come 8 / 0 = error or E.......???
Because division by zero, is not allowed in math.
Why?
-----
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.

4. Actually, to be honest, the Physics answer is that is can't be done on a calculator.

-Dan

5. Originally Posted by sonymd23
0 / 8 = 0
but how come 8 / 0 = error or E.......???
Hello, 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
$\frac{4}{4}=\frac{8}{8}=\frac{-1}{-1}=\frac{0}{0}=1$

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

$\frac{5\ \cdot \ 0}{0}=\frac{0}{0}$. 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

6. ## PH's second point

Originally Posted by sonymd23
0 / 8 = 0

but how come 8 / 0 = error or E.......???
Try writing it out in an equation, such as...
$\frac{5}{0}=x$

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

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

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

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

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

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

solve: $5\infty=0$

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 $\frac{x}{0}$

7. Originally Posted by Quick
Try writing it out in an equation, such as...
$\frac{5}{0}=x$

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

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

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

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

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

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

solve: $5\infty=0$

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 $\frac{x}{0}$
If anyone did such a calculation in front of me.... let me stop there.

Never, have I seen such an informal argument.

8. Originally Posted by ThePerfectHacker
If anyone did such a calculation in front of me.... let me stop there.

Never, have I seen such an informal argument.
Originally Posted by Attempting to Annoy Hacker
you can't divide by zero because someone out there says so.

9. Originally Posted by High School Teacher
you can't divide by zero because someone out there says so.
When I was younger that bothered me too. Because, I never knew the 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 $a/b=\sqrt{2}$ because you will not be able to. You might not know the reason but you place faith into the mathematicians and never try.

10. Originally Posted by ThePerfectHacker
Same thing as saying, do not try to find $a/b=\sqrt{2}$ because you will not be able to. You might not know the reason but you place faith into the mathematicians and never try.
It's not that I don't have faith in mathematicians, it's that the easiest way for me to remember things is to know why they are.
also, I assume you mean that a and b have to be rational numbers.

11. Originally Posted by Quick
Originally Posted by ThePerfectHacker
Same thing as saying, do not try to find $a/b=\sqrt{2}$ because you will not be able to. You might not know the reason but you place faith into the mathematicians and never try.
It's not that I don't have faith in mathematicians, it's that the easiest way for me to remember things is to know why they are.
also, I assume you mean that a and b have to be rational numbers.
There are no such integers is sufficient, that there are no such rationals
is implied by there being no such integers.

RonL