nitinz570 Group Title Having a conceptual problem why is 0/0 undefined? one year ago one year ago

1. nitinz570 Group Title

2. lgbasallote Group Title

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

3. panlac01 Group Title

indeterminate

4. nitinz570 Group Title

what that does mean actually? @lgbasallote

5. TuringTest Group Title

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

6. lgbasallote Group Title

the value cannot be determined...thus INdeterminate

7. nitinz570 Group Title

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

8. lgbasallote Group Title

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 Group Title

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

10. panlac01 Group Title

already sent him info on indeterminate

11. TuringTest Group Title

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 Group Title

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

13. SUROJ Group Title

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 Group Title

@SUROJ (0/0) is not undefined

15. lgbasallote Group Title

undefined is x/0

16. SUROJ Group Title

@lgbasallote why x/0 is undefined? curious

17. lgbasallote Group Title

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 Group Title

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 Group Title

nope

20. lgbasallote Group Title

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

21. TuringTest Group Title

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 Group Title

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 Group Title

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

24. TuringTest Group Title

@dumbcow

25. dumbcow Group Title

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

26. panlac01 Group Title

1/0 is not indeterminate

27. TuringTest Group Title

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

28. waterineyes Group Title

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 Group Title

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

30. panlac01 Group Title

1/0 is complex infinity

31. TuringTest Group Title

0^0 debated at times

32. waterineyes Group Title

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

33. panlac01 Group Title

yep

34. panlac01 Group Title

indeterminate*

35. panlac01 Group Title

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

36. SUROJ Group Title

there are 7 indeterminate forms in nature

37. panlac01 Group Title

just check wolfram mathworld.

38. TuringTest Group Title

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

39. SUROJ Group Title

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

40. panlac01 Group Title

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

41. TuringTest Group Title
42. panlac01 Group Title
43. TuringTest Group Title

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 Group Title

*some* mathematicians - I meant above...

45. TuringTest Group Title

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

46. TuringTest Group Title

to*

47. panlac01 Group Title

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

48. TuringTest Group Title

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

49. panlac01 Group Title

trust me, it does to me also

50. Herp_Derp Group Title

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 Group Title

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 Group Title

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