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nitinz570
Having a conceptual problem why is 0/0 undefined?
@Callisto @TuringTest please help ...
0/0 is not undefined...it is indeterminate
what that does mean actually? @lgbasallote
this is not an easy question to answer it has to do with different ways you can approach this limit
the value cannot be determined...thus INdeterminate
Oh no problem @TuringTest , I understand the problem @lgbasallote thanks a lot
there are a few main reasons why: 1) it conflicts between the rule that a number divided by itself is 1; and the rule that 0 divided by anything is 0. thus it conflicts whether the value is 1 or 0. so you cant determine if it is 1 or 0. 2) another reason is because there are infinite values that will give you 0 when multiplied by 0. so you cant determine which number is the right one.
Well @mathslover Recommend this site .. how to use this?
already sent him info on indeterminate
for example\[\lim_{x\to0}\frac xx=1\]but\[\lim_{x\to0}\frac{2x}x=2\]but both are mathematically equivalent to \[\frac00\]in the l;imit hence if we admitted\[\frac00\]into the set of numbers and gave it a value it would be inconsistent in mathematics and destroy the whole system effectively.
\[\lim_{x\to0}\frac{x^2}x=0\]etc. it would be an "inconsistent formal system"
to easily understand this concept let's take an example of (10/2) which is same as 5, and (5/5) is same as 1, but we can't say (0/0) as 1 simply because 0 on numerator is equal to zero on denominator, and (0/0) is undefined..... we don't know what it is.
@SUROJ (0/0) is not undefined
@lgbasallote why x/0 is undefined? curious
okay let's say for example x = 2 2/0 can you give me a number that when you multiply to 0 the answer is 2?
I think that technically both are undefined 1/0 is undefined but *not* an indefinite form 0/0 is an indefinite form. Is it also undefined? I think so...
i think the best term for 0/0 is indeterminate..
any division by zero is undefined, so x/0 is undefined 1/0 undefined and not indefinite 0/0 undefined and indefinite that's my understanding
my way of thinking is undefined refers to an infinite number that is not defined but we relatively know its really big or really small(big negative) indeterminate means we have no idea what the value is
I meant "indeterminate" when I said "indefinite" :/ so do you say that 1/0 is indeterminate or not?
no i would say its not indeterminate because we know the limit of 1/x as x->0 is infinity
1/0 is not indeterminate
ok I agree with that just making sure we're all on the same page
0*1 = 0 0*2 = 0 0*dog = 0 0*nitinz570 = 0 can you tell particularly for what values you are getting 0..??
the indeterminate forms are: 0/0 inf/inf 0*inf
1/0 is complex infinity
0^0 debated at times
\(0^0\) is also undetermined..
see how the mayan's gave mathematicians more to debate about?
there are 7 indeterminate forms in nature
just check wolfram mathworld.
mathematicians debate whether or not \(0^0=1\) or not Euler, for instance, thought it did
0/0, infinity/infinity, 0^infinity, 1^infinity, 0^0, infinity^0, infinity-infinity
if 0^0 =1 then 0/0 = 1 also
http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/?PHPSESSID=40fdcce21f158a5d17267b711e395947#b not true panlac
mathematicians *define* \(0^0=1\) because of a number of arguments btw note that your reference is Thomas and Finney 1996, pp. 220 and 423; Gellert et al. 1989, p. 400 and there are other equally reputable books and references that disagree if you read the article I linked you too, or some of those linked to it.
*some* mathematicians - I meant above...
it is just very debated ti this day is all I generally treat it as undefined as well
yeh. my math professor is one of those who thinks the same way. but she teaches it as indeterminate
It makes more sense to me as well, I'm just pointing out the discrepancy out there...
trust me, it does to me also
For x not equal to 0, x/0 is defined (as a number, not necessarily as a limit) in a 1-point compactification of the reals (the projectively extended real numbers) or the complex numbers (the extended complex plane), and is equal to infinity. However, 0/0 (as a number) is still undefined in these settings.
btw the limit of x^x as x->0 is 1 , which i believe is a strong argument for equating 0^0 to 1
Nice discussion and also : \[\huge{\mathbb{Welcome}\textbf{To}\mathbb{Open}\textbf{Study}}\]