## nitinz570 3 years ago Having a conceptual problem why is 0/0 undefined?

1. nitinz570

2. lgbasallote

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

3. panlac01

indeterminate

4. nitinz570

what that does mean actually? @lgbasallote

5. TuringTest

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

6. lgbasallote

the value cannot be determined...thus INdeterminate

7. nitinz570

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

8. 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.

9. nitinz570

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

10. panlac01

already sent him info on indeterminate

11. 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.

12. TuringTest

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

13. SUROJ

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.

14. lgbasallote

@SUROJ (0/0) is not undefined

15. lgbasallote

undefined is x/0

16. SUROJ

@lgbasallote why x/0 is undefined? curious

17. 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?

18. 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...

19. SUROJ

nope

20. lgbasallote

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

21. 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

22. 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

23. TuringTest

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

24. TuringTest

@dumbcow

25. dumbcow

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

26. panlac01

1/0 is not indeterminate

27. TuringTest

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

28. waterineyes

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

29. dumbcow

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

30. panlac01

1/0 is complex infinity

31. TuringTest

0^0 debated at times

32. waterineyes

$$0^0$$ is also undetermined..

33. panlac01

yep

34. panlac01

indeterminate*

35. panlac01

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

36. SUROJ

there are 7 indeterminate forms in nature

37. panlac01

just check wolfram mathworld.

38. TuringTest

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

39. SUROJ

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

40. panlac01

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

41. TuringTest
42. panlac01
43. 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.

44. TuringTest

*some* mathematicians - I meant above...

45. TuringTest

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

46. TuringTest

to*

47. panlac01

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

48. TuringTest

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

49. panlac01

trust me, it does to me also

50. Herp_Derp

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.

51. 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

52. mathslover

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