I usually like to think as division as "how many times something goes into something"
As we all know, putting anything/0 gives an error, and there are many memes involving it. But wouldn't the answer HAVE to be zero? Zero goes into anything (other than zero) no times, so it would have to be zero for every number except 0, which is 1.
If its too confusing:
0 goes into anything other than 0 no times, 0 goes into 0 1 time. Shouldn't anything/0 = 0?
Mathematicians have a precise definition for division, and it is NOTHING like yours. Try looking at it sometime.
In my field (computer science), we generally define it as what is the most useful for the situation. Sometimes we substitute infinity, sometimes we throw an error, sometimes we branch off to another part of the software and do something different.
IMO, math is just one of the tools of the trade, and the important thing is to use it in a way that makes sense for what you are doing.
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When all is said and done, Will you have said more than you have done?
In my field (computer science), we generally define it as what is the most useful for the situation. Sometimes we substitute infinity, sometimes we throw an error, sometimes we branch off to another part of the software and do something different.
Well, this is because we have to do something with it. It can't pass through too many layers of abstraction or else your program will end up shitting itself. We are bound by the physical capabilities of the CPU, and so we have to make do.
well e^(iπ) is negative one. Add one and you get zero, which gives 1 divided by zero. What did you mean by "get anywhere"?
I think he's asking if throwing that into a problem rather than zero would change the result.
well then the answer is no, it does not change the value since it is 0. It could change limits though if it was applied as a linear transformation to the originating function.
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To those who pointed out that any (nonzero) number divided by zero is infinity, this is actually not quite true. It's greater than infinity. For example, if 2 / 0 = ∞, then we'd expect 0 * ∞ to equal 2. But it doesn't. It still equals 0. So even an infinite number of zeros isn't enough. You need more....
To those who pointed out that any (nonzero) number divided by zero is infinity, this is actually not quite true. It's greater than infinity. For example, if 2 / 0 = ∞, then we'd expect 0 * ∞ to equal 2. But it doesn't. It still equals 0. So even an infinite number of zeros isn't enough. You need more....
...To infinity, and beyond!!
Not really. Infinity isn't a number so you can't (at least from my understanding of it) perform arithmetic with it. I know when talking about limits infinity*0 is indeterminate, because it depends on "how fast" its going to infinity and how fast its going to 0.
Anyway, 2/0 doesn't = 0, it's error.
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As you get smaller and smaller (closer and closer to 0), the number resulting gets larger and larger. This makes sense right? However, it would take infinite iterations of what I was just doing to reach zero. Infinite iterations of something that gets bigger on each iteration implies that a number is increasing infinitely, in other words... anything divided by 0 is infinity. Just as you can never reach infinity, you can never reach anything divided by 0. Infinity is always undefined, but undefined is not always infinity.
As you get smaller and smaller (closer and closer to 0), the number resulting gets larger and larger. This makes sense right? However, it would take infinite iterations of what I was just doing to reach zero. Infinite iterations of something that gets bigger on each iteration implies that a number is increasing infinitely, in other words... anything divided by 0 is infinity. Just as you can never reach infinity, you can never reach anything divided by 0. Infinity is always undefined, but undefined is not always infinity.
Undefined is just that, undefined. There is no magic formula to turn one divided by zero into infinity. The concept you describe is a limit, which says that as x becomes sufficiently close to c, f(x) becomes sufficiently close to L. Notice that it is only "sufficiently close" to a value, but not actually that value.
The example above will always return infinity when you put in 1/0 :smile.gif:.
Debating the philosophy behind 1/0 seems a tad pointless anyways. In most practical applications (engineering, computer programming, etc) you simply treat it as a special case and do what makes sense when you encounter it. There's usually a reasonable way to handle it.
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When all is said and done, Will you have said more than you have done?
Should do it. Since you don't have limits headed in opposite directions, the result is clearly positive infinity.
That's only true if you're willing to get an answer that isn't in the set of real numbers. Depending on context that may or may not be okay. It doesn't change the fact that 1/0 is simply undefined in the real numbers (though it *is* defined in the projective real line and in that case it's defined to be the point at infinity).
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There is no magic formula to turn one divided by zero into infinity.
Should do it. Since you don't have limits headed in opposite directions, the result is clearly positive infinity.
No, the result of taking the limit is clearly positive infinity. As Yourself said, 1/0 is still undefined in your case for the set of all real numbers.
Division already has a precise definition. And, by definition, you can't divide by zero.
Mathematicians have a precise definition for division, and it is NOTHING like yours. Try looking at it sometime.
So 1/e^iπ+1?
well e^(iπ) is negative one. Add one and you get zero, which gives 1 divided by zero. What did you mean by "get anywhere"?
I think he's asking if throwing that into a problem rather than zero would change the result.
You heard that, green and red.
IMO, math is just one of the tools of the trade, and the important thing is to use it in a way that makes sense for what you are doing.
Well, this is because we have to do something with it. It can't pass through too many layers of abstraction or else your program will end up shitting itself. We are bound by the physical capabilities of the CPU, and so we have to make do.
well then the answer is no, it does not change the value since it is 0. It could change limits though if it was applied as a linear transformation to the originating function.
...To infinity, and beyond!!
Not really. Infinity isn't a number so you can't (at least from my understanding of it) perform arithmetic with it. I know when talking about limits infinity*0 is indeterminate, because it depends on "how fast" its going to infinity and how fast its going to 0.
Anyway, 2/0 doesn't = 0, it's error.
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You are almost correct. 0/0, ∞ / ∞, and 0 * ∞ can all be managed using L'Hopital's Rule, but only in the scope of finding limits in calculus.
Yeah but he's not talking about limits. There's not function that can be measured as x->infinity or anything, just 2 numbers.
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1/1 < 1/0.1 < 1/0.01 < 0.001....
As you get smaller and smaller (closer and closer to 0), the number resulting gets larger and larger. This makes sense right? However, it would take infinite iterations of what I was just doing to reach zero. Infinite iterations of something that gets bigger on each iteration implies that a number is increasing infinitely, in other words... anything divided by 0 is infinity. Just as you can never reach infinity, you can never reach anything divided by 0. Infinity is always undefined, but undefined is not always infinity.
Undefined is just that, undefined. There is no magic formula to turn one divided by zero into infinity. The concept you describe is a limit, which says that as x becomes sufficiently close to c, f(x) becomes sufficiently close to L. Notice that it is only "sufficiently close" to a value, but not actually that value.
1/abs(x)
Should do it. Since you don't have limits headed in opposite directions, the result is clearly positive infinity.
If you want a programmatic solution (pseudocode):
divide(x, y)
{
if(y==0)
{
return infinity;
} else
{
return x/y;
}
The example above will always return infinity when you put in 1/0 :smile.gif:.
Debating the philosophy behind 1/0 seems a tad pointless anyways. In most practical applications (engineering, computer programming, etc) you simply treat it as a special case and do what makes sense when you encounter it. There's usually a reasonable way to handle it.
That's only true if you're willing to get an answer that isn't in the set of real numbers. Depending on context that may or may not be okay. It doesn't change the fact that 1/0 is simply undefined in the real numbers (though it *is* defined in the projective real line and in that case it's defined to be the point at infinity).
No, the result of taking the limit is clearly positive infinity. As Yourself said, 1/0 is still undefined in your case for the set of all real numbers.