limit as x approaches zero for 1/x does equal infinity
but 1/0 is jackshit
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Anonymous2006-08-19 6:06
1/x does tend to infinity as x approaches 0, but it is undefined because it would break the laws of arithmetic, in the way other people in this thread have been doing.
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Anonymous2006-08-19 6:14
0 isn't a real number
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Anonymous2006-08-19 9:31
No number is a real number
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Anonymous2006-08-19 10:47
>>9
Any number less than or above 0, more than minus infinity and less than infinity is a number.
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Anonymous2006-08-19 18:10
>>7
That's why >>6 is explaining why people think so by using limits, not regular arithmetic. It's defined as infinity when you use limits, but plain 1/0 IS undefined.
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Anonymous2006-08-19 19:30
It doesn't break the laws of arithmetic ...
x/0 = infinity makes perfect sense
But then you have to decide whether infinity has a sign; hence the extended real number line (which has +inf and -inf) versus the real projective number line (which just has an inf which is both positive and negative and neither at the same time). The extended real number line sort of doesn't make sense because the sign of the result you get in taking the limit varies depending upon which side you approach it from. However, the definitions of +/-inf are very useful in calculus and suchlike, and so it is commonly used.
IEEE754 (the standard for floating point numbers) defines:
|x|/0 = infinity
-|x|/0 = -infinity
And 0/0 is truly undefined: IEEE754 gives 0/0 = NaN (not a number).
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Anonymous2006-08-19 20:10
>>12
Protip: we aren't talking about floating point numbers.
>>12
PROTIP: The x/0 problem is not an arithmetic problem. You can't divide something by zero. You can however take the limit as the denominator approaches zero, and the number will approach infinity.
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Anonymous2006-08-19 21:17
PROTIP: It was an arithmetic problem. You can't divide something by the sign of the result you get in taking the limit. You can however, the definitions of +/-inf are very useful in calculus and the number will approach infinity.
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Anonymous2006-08-19 21:32
>>16
PROTIP: Learn how to form a coherent sentence. It will help you in your quest.
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Anonymous2006-08-19 21:35
>>14
A completely irrelevant example which does absolutely nothing but bring doubt to the credibility of your claim that "defining" 1/0 = infinity does not affect the reals, as floating point numbers do not form a field as the reals do.
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Anonymous2006-08-20 3:34
1/0 can equal all reals....so in that instance yet it can equal infinity because the number of products is infinite
I don't thinkhe ever said that defining 1/0 = infinity doesn't affect the reals .......
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Anonymous2006-08-20 9:17
1/0=infinity
thus 1=0*infinity.
But 0*anything=0
So 1=0?
NO. see the problem of ignoring the limit? all these math problems on this forum come from dipshits who know little about math except what their high school teacher told them that math was bullshit because...(e.g. 0.999...not= 1).
>>20
Congratulations on being extraordinarily anal. You never said it does not affect the reals, you said it does not affect/break the laws of arithmetic (of the reals). It does. Specifically, if you take Reals U {infinity} and define 1/0 = infinity, then you no longer have a field. There may be non-standard models of the reals (NSA is not an area I'm particularly interested in) which do extend the reals with infinity and maintain the properties of a field, but they still do not define 1/0.
Be sure to scroll down to get a long list of all the arithmetic operations that make no fucking sense with infinity. The extended reals are useless.
Oh, and by the way:
And 0/0 is truly undefined: IEEE754 gives 0/0 = NaN (not a number).
0/0 is not undefined, it's indeterminate. Fucking fail for thinking a bunch of engineering standards properly define mathematics.
0/0 is not undefined, it's indeterminate. Fucking fail for thinking a bunch of engineering standards properly define mathematics.
Weren't L'Hopital and such theorems just an old form of RFCs?
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Anonymous2006-08-21 11:46
0/0 is undefined. Fucking fail for not knowing algebra terminology.
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Anonymous2006-08-21 15:50
ITT 4CHAN'S OBESSION WITH DIVIDE BY ZERO!
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Anonymous2006-08-22 3:43
if 0/0 is undefined any#/0 is undefined. where's the problem?
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Anonymous2006-08-22 6:13
0/0 is indeterminate when you're using limits. if x=0 and you have x/x then it is 1. 7x/x = 7. It's indeterminate because you need more information to determine the answer.