Having a conceptual problem
why is 0/0 undefined?

- anonymous

Having a conceptual problem
why is 0/0 undefined?

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- schrodinger

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- anonymous

@Callisto @TuringTest please help ...

- lgbasallote

0/0 is not undefined...it is indeterminate

- anonymous

indeterminate

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## More answers

- anonymous

what that does mean actually? @lgbasallote

- TuringTest

this is not an easy question to answer
it has to do with different ways you can approach this limit

- lgbasallote

the value cannot be determined...thus INdeterminate

- anonymous

Oh no problem @TuringTest , I understand the problem
@lgbasallote thanks a lot

- lgbasallote

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.

- anonymous

Well @mathslover Recommend this site ..
how to use this?

- anonymous

already sent him info on indeterminate

- TuringTest

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.

- TuringTest

\[\lim_{x\to0}\frac{x^2}x=0\]etc.
it would be an "inconsistent formal system"

- anonymous

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.

- lgbasallote

@SUROJ (0/0) is not undefined

- lgbasallote

undefined is x/0

- anonymous

@lgbasallote why x/0 is undefined? curious

- lgbasallote

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?

- TuringTest

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...

- anonymous

nope

- lgbasallote

i think the best term for 0/0 is indeterminate..

- TuringTest

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

- dumbcow

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

- TuringTest

I meant "indeterminate" when I said "indefinite" :/
so do you say that 1/0 is indeterminate or not?

- TuringTest

@dumbcow

- dumbcow

no i would say its not indeterminate because we know the limit of 1/x as x->0 is infinity

- anonymous

1/0 is not indeterminate

- TuringTest

ok I agree with that
just making sure we're all on the same page

- anonymous

0*1 = 0
0*2 = 0
0*dog = 0
0*nitinz570 = 0
can you tell particularly for what values you are getting 0..??

- dumbcow

the indeterminate forms are:
0/0
inf/inf
0*inf

- anonymous

1/0 is complex infinity

- TuringTest

0^0 debated at times

- anonymous

\(0^0\) is also undetermined..

- anonymous

yep

- anonymous

indeterminate*

- anonymous

see how the mayan's gave mathematicians more to debate about?

- anonymous

there are 7 indeterminate forms in nature

- anonymous

just check wolfram mathworld.

- TuringTest

mathematicians debate whether or not \(0^0=1\) or not
Euler, for instance, thought it did

- anonymous

0/0, infinity/infinity, 0^infinity, 1^infinity, 0^0, infinity^0, infinity-infinity

- anonymous

if 0^0 =1 then 0/0 = 1 also

- TuringTest

http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/?PHPSESSID=40fdcce21f158a5d17267b711e395947#b
not true panlac

- anonymous

http://mathworld.wolfram.com/Indeterminate.html

- TuringTest

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.

- TuringTest

*some* mathematicians - I meant above...

- TuringTest

it is just very debated ti this day is all
I generally treat it as undefined as well

- TuringTest

to*

- anonymous

yeh. my math professor is one of those who thinks the same way. but she teaches it as indeterminate

- TuringTest

It makes more sense to me as well, I'm just pointing out the discrepancy out there...

- anonymous

trust me, it does to me also

- anonymous

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.

- dumbcow

btw the limit of x^x as x->0 is 1 , which i believe is a strong argument for equating 0^0 to 1

- mathslover

Nice discussion and also :
\[\huge{\mathbb{Welcome}\textbf{To}\mathbb{Open}\textbf{Study}}\]

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