## abdul_shabeer Group Title 100000000000................ continues infinitely. Is it a number? one year ago one year ago

1. KaylaBrewington Group Title

yes because the number line never stops

2. sauravshakya Group Title

|dw:1349359330358:dw| Is infinity a number?

3. experimentX Group Title

not a natural number and not real number either.

4. chandhuru Group Title

infinity is something which cant be defined...

5. experimentX Group Title

no .. irrational number is a real number.

6. abdul_shabeer Group Title

Is it a number?

7. sauravshakya Group Title

IS infinity a number?

8. experimentX Group Title

it's a number is http://en.wikipedia.org/wiki/Hyperreal_number and http://en.wikipedia.org/wiki/Surreal_number ... I don't know much about this ... but this is not a real number and natural number.

9. experimentX Group Title

*in

10. sauravshakya Group Title

If 100000000000000... is not a natural number then the set of natural number is finite. right?

11. chandhuru Group Title

@experimentX how do u say that it is not a real number??

12. experimentX Group Title

no ... the set of natural number is infinite but does not contain infinity.

13. TuringTest Group Title

Infinity is a concept, not a number (I know I'm basically just restating, but it is worth emphasizing)

14. experimentX Group Title

you always write |dw:1349359774760:dw|

15. experimentX Group Title

you should have noted.

16. abdul_shabeer Group Title

then why 1/3 is considered a number?

17. TuringTest Group Title

0.3333.... as the 3's continue the number is not getting any bigger, as opposed to making an infinitely number before the decimal which would create an infinitely large number.

18. TuringTest Group Title

hm... I phrased that poorly :/

19. experimentX Group Title

natural number is defined as inductive set that begins with 1 and |dw:1349359861034:dw|

20. TuringTest Group Title

indeed what would 10000.....+1 be? could you write it? where would you put the 1 ?

21. abdul_shabeer Group Title

Why 0.333333333333333333....... is a number?

22. TuringTest Group Title

that is different from 0.3333....+1=1.3333... not problem there

23. experimentX Group Title

1/3 is repetitive ... if you take 1m string ... fold it thrice, you can always pinpoint this is 1/3 . Therefore it lies inside real number line.

24. TuringTest Group Title

you can add any number to 0.333.... and create a new number on the real line where would 1000...+1 be on the real line if you can point it out then I will let you call it a number ;)

25. TuringTest Group Title

I like this video to help with understanding repeating decimals, though it does not directly answer your question http://www.youtube.com/watch?v=TINfzxSnnIE

26. chandhuru Group Title

@abdul_shabeer u can find the number 0.333333333 or atleast u can locate the point 0.33333 number between 3 and 4 , but u cant locate the infinity .......

27. abdul_shabeer Group Title

We can't locate 0.333333.......

28. TuringTest Group Title

yes we can

29. chandhuru Group Title

atleast u know that 0.33333 is present between 0.3 and 0.4 .... in case of infinity u cant ...... can u ????

30. TuringTest Group Title

|dw:1349360426152:dw|

31. TuringTest Group Title

now you show me what two numbers 1000..... lies between :)

32. abdul_shabeer Group Title

What is (0.333333......)* 10?

33. TuringTest Group Title

3.333333...

34. abdul_shabeer Group Title

0.333..... * 10 = 0.333...+0.3333....+0.3333....( 10 times) Can we add this?

35. TuringTest Group Title

I think it is a lot easier to see it as 1/3+1/3+1/3+...(ten times) =10/3

36. abdul_shabeer Group Title

I want to add it without converting it into 1/3

37. TuringTest Group Title

why?

38. abdul_shabeer Group Title

As 0.3333.... = 1/3, in whichever way i add I must get the same result

39. Razzputin Group Title

100000000000......... lies between 99999999999...... and 11000000000000...... where all three of the numbers stretch out infinitly.

40. TuringTest Group Title

0.333...+0.333...=0.666... 0.666...+0.333...=0.999... 0.999...+0.333...=1.222... do that ten times and you will get 3.333...

41. TuringTest Group Title

and @Razzputin that is wrong, how can you show me that 9999... is not bigger than 1000... ?

42. abdul_shabeer Group Title

How 0.999...+0.333...=1.222...?

43. TuringTest Group Title

are there more digits in one number or the other? no

44. Razzputin Group Title

what if you where to state that 999.... was 1 less than infinite?

45. TuringTest Group Title

ad a 3 to each 9

46. TuringTest Group Title

47. TuringTest Group Title

48. TuringTest Group Title

the 1's carry over

49. abdul_shabeer Group Title

|dw:1349364346874:dw|

50. abdul_shabeer Group Title

and the last digit would be 2

51. TuringTest Group Title

yeah but there are an infinite number of 3's and 9's so every digit carries a one from the previous decimal place

52. TuringTest Group Title

there is no last digit, that's why it's an infinitely repeating decimal

53. abdul_shabeer Group Title

There is no last digit, I just took a small value

54. TuringTest Group Title

which makes it not the same as 1/3+1 which is what you are trying to do

55. TuringTest Group Title

$0.333\neq0.333...=1/3$

56. TuringTest Group Title

this is why we don't add numbers with infinite decimals very often; It's ugly, confusing, and entirely unnecessary

57. abdul_shabeer Group Title

what do you get when you add 0.9999...+0.3333... without taking 0.99999...=1 and 0.333... = 1/3

58. TuringTest Group Title

math is about making things as simple as possible, not over-complicating things and I told you 0.999....+0.333...=1.333... ^ why is this not a 2? because there is another 3 after it, though we did not write it and another after that, and another after that, ad infinitum

59. TuringTest Group Title

at no point does the decimal terminate, hence EVERY digit carries a 1 from the digit after it

60. abdul_shabeer Group Title

But still you just can't neglect a 2

61. TuringTest Group Title

yes you can because there is absolutely no 2 how many decimal points down would you expect to find it?

62. abdul_shabeer Group Title

Which means it is not equal to 1+ 0.3333....

63. TuringTest Group Title

it would have to be in the same decimal place as the remaining 1 you might expect by subtracting 1-0.999... you might say, "well where is the remaining 1?" well, it is literally *infinitely* far down the decimal, which means it ain't there

64. TuringTest Group Title

how do you figure that 0.999...+0.333... is not the same as 1+0.333... ?

65. abdul_shabeer Group Title

66. TuringTest Group Title

so?

67. TuringTest Group Title

you want to start at the far right side I presume? but what is the farthest right digit, and what decimal place is it in?

68. TuringTest Group Title

you are trying to use math skill you learned in grade school to deal with simple, finitely long numbers on an infinitely long decimal representation

69. abdul_shabeer Group Title

How do you add two numbers?

70. TuringTest Group Title

either by grasping the concept that there is no last digit and recognizing that the 1 will ALWAYS carry over from the previous digit, or by representing it as a fraction which is perfectly valid an makes life way easier

71. TuringTest Group Title

I suggest you stop trying to hurt your brain dealing with infinitely long decimals and and work on deepening your understanding as to why these infinite decimals are exactly equivalent to fractions

72. abdul_shabeer Group Title

0.9999.... = 1, I want to disprove this

73. TuringTest Group Title

you can't disprove something that is true

74. abdul_shabeer Group Title

Can you prove it?

75. TuringTest Group Title

again, what is 1-0.999... ?

76. TuringTest Group Title

prove it? yes would you like me to?

77. abdul_shabeer Group Title

yes

78. TuringTest Group Title

$x=0.\overline9$$10x=9.\overline9$$10x-x=9x=9$$x=1$

79. abdul_shabeer Group Title

0.999...*10 = 0.999...+0.999...+0.999...(10 times) How do you add this?

80. TuringTest Group Title

again, the way I showed you adding 0.333... every time we get the following succession 0.333... 0.666... 0.999... 1.333... 1.666... 1.999... 2.333... 2.666... 2.999... 3.333...

81. abdul_shabeer Group Title

But what about the last digit. Though we don't get till last digit we observe that the last digit gets a different value

82. TuringTest Group Title

oh I did it with 0.333... but the idea is the same

83. TuringTest Group Title

where is this mythical last digit? what decimal place is it in? the tens, the thousands, the ten-millions?

84. TuringTest Group Title

what is the last digit of pi?

85. abdul_shabeer Group Title

It is an irrational number

86. TuringTest Group Title

but the point is the same, where is the last digit of 0.999... ? what decimal place is it in?

87. abdul_shabeer Group Title

88. TuringTest Group Title

normally, from right to left but this is not a comparable problem because each number has a last digit, which is where you start adding from can you do that if there is *no last digit*???

89. TuringTest Group Title

how can you start at the far right when there is no far right? you can't

90. abdul_shabeer Group Title

But you say that 0.3333..... is a rational number

91. TuringTest Group Title

yes and I can prove it what is your point?

92. abdul_shabeer Group Title

When you can't start at the far right, how do you take 0.999...*10 = 9.999...

93. TuringTest Group Title

by having a deeper understanding of what it means to add two infinitely long decimal representations, or by understanding that this is the same as 1*10 your grade school adding methods are powerless here, you must accept that

94. abdul_shabeer Group Title

Why it is same as 1*10?

95. TuringTest Group Title

because 0.999...=1

96. abdul_shabeer Group Title

What is the standard way of adding two numbers?

97. abdul_shabeer Group Title

98. TuringTest Group Title

brb @experimentX feel free to take over if you like I will be back in a sec

99. experimentX Group Title

i lost track of it ... looks like conversation reached almost infinity ... where do you have problem?

100. abdul_shabeer Group Title

What is the standard way of adding two numbers?

101. experimentX Group Title

102. abdul_shabeer Group Title

103. experimentX Group Title

draw a real line .. |dw:1349367528137:dw|

104. experimentX Group Title

|dw:1349367566686:dw|

105. abdul_shabeer Group Title

How would you add 0.999.... and 0.333...?

106. TuringTest Group Title

I would agree that is a good standard way to think of addition^ but you want to do 0.333...+0.999... in which case you have to observe a pattern, which you seem to be reluctant to accept

107. experimentX Group Title

you can always locate these points on the real line. and if you continue 0.999.... .... to up infinity this is 1 and for 0.33333.... you might think that you can never locate this point on real line. you can actually locate it. and there is ONE and only ONE point on the line i drew. add these distances.

108. abdul_shabeer Group Title

This problem started in the proof of 0.999... = 1

109. experimentX Group Title

yeah ... it seems that this is not equal to 1 ... but if you continue this up to infinity ... still this is non intuitive. here a short reason to believe. 0.9 ~ 1.1 <--- let's find a pair of points 0.99 ~ 1.01 0.999 ~ 1.001 <--- 0.9999 ~ 1.0001 <--- in similar fashion you put infinite zeros between 1 and the last 1 what would you get 1.00000000000.. infinite zeros.....................1

110. TuringTest Group Title

to do 0.999...*10 you can either 1) accept that multiplication by 10 moves the decimal place over by one space (it is perfectly okay to utilize that, if we did not utilize powerful concepts as givens then math would be a monstrosity to do!) or 2) add each corresponding digit ten times and recognize that there is not last digit, hence every digit will carry a one from the digit to its right, of which there are infinitely many I strongly suggest option 1

111. abdul_shabeer Group Title

Multiplication by 10 is nothing but adding it 10 times

112. experimentX Group Title

if you say this is 1 1.00000000000.. infinite zeros.....................1 then this must be equal to 1 too 0.99999999999999.... infinite nines

113. TuringTest Group Title

or as I put it, 1-0.999...=? if we say 1-0.999...=0.000...1 in what decimal place would the 1 be? infinitely far out, i.e. there isn't one

114. experimentX Group Title

I think you are misunderstanding infinity with undefined, infinity is greater than you imagine.

115. experimentX Group Title

1.00000000000.. infinite zeros.....................1 this means 1.00000000000.. here are more zeros than you imagine ....................1

116. TuringTest Group Title

@abdul_shabeer if you want to utilize option 2 that is fine, but be careful about how the digits carry over from infinitely far to the right

117. abdul_shabeer Group Title

You mean something which is at infinity is not there.

118. TuringTest Group Title

don't play fast and loose with ideas like "infinity means it's not there" this is a subtle and tricky issue, and cannot be captured in a phrase like that

119. experimentX Group Title

yep. kinda something like that http://math.stackexchange.com/questions/11/does-99999-1 also that video by ViHart is very nice ... but few the argument she used had been downvoted quite badly on MSE. Let the experts know.

120. abdul_shabeer Group Title

Do you remember the question on whether a point is dimensionless? If we compare the size of earth with universe, how big do you think the earth would be?

121. TuringTest Group Title

the same size it would be if the universe was only as big as the solar system comparison does not make a thing bigger or smaller

122. abdul_shabeer Group Title

if you are out of Milky way and you look at earth, would you be able to find it?

123. estudier Group Title

If it isn't 1 * 10^n, what is it?

124. TuringTest Group Title

with the right equipment, theoretically yes

125. abdul_shabeer Group Title

With no equipments

126. TuringTest Group Title

with the human eye (which is a piece of equipment itself in many respects)? no of course not, why does that matter?

127. abdul_shabeer Group Title

If we see the space out of earth, would it appear like a 2D image?

128. TuringTest Group Title

the ancients thought it was, so I guess you could argue yes, but that is just a matter of the limitations of human perception

129. TuringTest Group Title

there is no obvious perspective point in the night sky, so our brains don't do so well gauging distance why are we talking about this all of a sudden?

130. abdul_shabeer Group Title

Okay Thank You Max and ExperimentX

131. TuringTest Group Title

very welcome!

132. experimentX Group Title

no probs at all ...