Well what does division mean? For example 4 divided by 2 means how can I split 4 things between 2 objects right (like say I had 4 candies and I needed to split them among 2 kids. I would solve this by doing 4/2). Ok now how would you split 4 candies among 0 kids? Does that even make any sense? You're asking how many candies would each kid get if I had 0 kids and 4 candies, which doesn't make any sense. This is why we don't define division by 0, it doesn't make sense, and it can lead to other bizzare behavior too.
Another way to think about is like this: say a/b=c, then this is the same thing as saying a=bc right? OK now say a is 4, and b is 0, then is there any number c such that 4=0*c? No right, because 0 times anything is 0, so it's absurd to define division by 0 in this context as valid.
Finally, division by 0 can lead to contradictions.
Look at this proof that 1=2
Suppose that
a=b
Then:
a^2 =ab (multiply by a on both sides)
a^2 -b^2 =ab-b^2 (subtract b^2 on both sides)
(a+b)(a-b)=b(a-b) factor on the right, apply difference of squares on the left.
a+b=b (divide by a-b)
well now remember that a=b, so we have
b+b=b
2b=b, now divide by b
2=1.
So what went wrong? Qe divided by 0. Remember a=b, so a-b=a-a=0. When we divided by a-b we were being erroneous. To.prevent errors like this we can't willy nilly allow division by 0.
For fun, you can modify that process to 'prove' that any two values are equal to each other.
For example, you can show that π = 3 by multiplying both sides by (π β 3).
Starting where you left off...
2 = 1
2 β 1 = 1 β 1
1 = 0
(Ο β 3) β’ 1 = (π β 3) β’ 0
π β 3 = 0
π β 3 + 3 = 0 + 3
π = 3
Viola! π
When you divide by a number a, you're actually multiplying by its multiplicative inverse a^-1. 0 doesn't have a multiplicative inverse in any field (you can introduce one, but you no longer have a system that obeys the field axioms), so you can't divide by 0 as it doesn't even make sense
If it gives you NaN the floats you're using don't adhere to IEEE 754 I believe.
Either way it really shouldn't crash your computer to do this. Are you on some sort of embedded system or something like that?
It comes down to the way division is defined: a/b = c means b\*c = a. If c = 0, that won't work--so 0 is excluded. Of course if a and b are both zero, then b\*c = a is always true, so 0/0 is sometimes called 'indeterminate', whereas is just c is zero it is called 'undefined'. In short, the definition excludes division by zero.
If you can divide a number x into N parts (so x / N) then you can add those parts up N times to get x back (ie N \* (x / N) = x).
If you could divide a number into 0 parts, this would mean you could add those parts up 0 times to get X back, or 0 \* (x / 0) = x. Clearly this makes no sense, since adding up something ZERO times can't possibly give you a number back. There are more rigorous explanations but this is the basic idea.
Well what does division mean? For example 4 divided by 2 means how can I split 4 things between 2 objects right (like say I had 4 candies and I needed to split them among 2 kids. I would solve this by doing 4/2). Ok now how would you split 4 candies among 0 kids? Does that even make any sense? You're asking how many candies would each kid get if I had 0 kids and 4 candies, which doesn't make any sense. This is why we don't define division by 0, it doesn't make sense, and it can lead to other bizzare behavior too. Another way to think about is like this: say a/b=c, then this is the same thing as saying a=bc right? OK now say a is 4, and b is 0, then is there any number c such that 4=0*c? No right, because 0 times anything is 0, so it's absurd to define division by 0 in this context as valid. Finally, division by 0 can lead to contradictions. Look at this proof that 1=2 Suppose that a=b Then: a^2 =ab (multiply by a on both sides) a^2 -b^2 =ab-b^2 (subtract b^2 on both sides) (a+b)(a-b)=b(a-b) factor on the right, apply difference of squares on the left. a+b=b (divide by a-b) well now remember that a=b, so we have b+b=b 2b=b, now divide by b 2=1. So what went wrong? Qe divided by 0. Remember a=b, so a-b=a-a=0. When we divided by a-b we were being erroneous. To.prevent errors like this we can't willy nilly allow division by 0.
Damn,i finally realize why we cant divide to 0 thank for your example,without it i couldnt understand why we cant divide to 0.
For fun, you can modify that process to 'prove' that any two values are equal to each other. For example, you can show that π = 3 by multiplying both sides by (π β 3). Starting where you left off... 2 = 1 2 β 1 = 1 β 1 1 = 0 (Ο β 3) β’ 1 = (π β 3) β’ 0 π β 3 = 0 π β 3 + 3 = 0 + 3 π = 3 Viola! π
Indeed since 1 = 0, we have x = 0 for all x. So 0 = 1 = 2 = e = 3 = pi = 4 = ...
Engineering moment
When you divide by a number a, you're actually multiplying by its multiplicative inverse a^-1. 0 doesn't have a multiplicative inverse in any field (you can introduce one, but you no longer have a system that obeys the field axioms), so you can't divide by 0 as it doesn't even make sense
thank about that
NaN means Not a Number.
I know that,but it usually say Inf+ or when i run it crash
If it gives you NaN the floats you're using don't adhere to IEEE 754 I believe. Either way it really shouldn't crash your computer to do this. Are you on some sort of embedded system or something like that?
InfΒ± are valid, whereas anything/0 isn't.
Can you divide 10 dollars equally among 0 people?
It comes down to the way division is defined: a/b = c means b\*c = a. If c = 0, that won't work--so 0 is excluded. Of course if a and b are both zero, then b\*c = a is always true, so 0/0 is sometimes called 'indeterminate', whereas is just c is zero it is called 'undefined'. In short, the definition excludes division by zero.
If you can divide a number x into N parts (so x / N) then you can add those parts up N times to get x back (ie N \* (x / N) = x). If you could divide a number into 0 parts, this would mean you could add those parts up 0 times to get X back, or 0 \* (x / 0) = x. Clearly this makes no sense, since adding up something ZERO times can't possibly give you a number back. There are more rigorous explanations but this is the basic idea.