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abdul_shabeer Group Title

100000000000................ continues infinitely. Is it a number?

  • one year ago
  • one year ago

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  1. KaylaBrewington Group Title
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    yes because the number line never stops

    • one year ago
  2. sauravshakya Group Title
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    |dw:1349359330358:dw| Is infinity a number?

    • one year ago
  3. experimentX Group Title
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    not a natural number and not real number either.

    • one year ago
  4. chandhuru Group Title
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    infinity is something which cant be defined...

    • one year ago
  5. experimentX Group Title
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    no .. irrational number is a real number.

    • one year ago
  6. abdul_shabeer Group Title
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    Is it a number?

    • one year ago
  7. sauravshakya Group Title
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    IS infinity a number?

    • one year ago
  8. experimentX Group Title
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    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.

    • one year ago
  9. experimentX Group Title
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    *in

    • one year ago
  10. sauravshakya Group Title
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    If 100000000000000... is not a natural number then the set of natural number is finite. right?

    • one year ago
  11. chandhuru Group Title
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    @experimentX how do u say that it is not a real number??

    • one year ago
  12. experimentX Group Title
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    no ... the set of natural number is infinite but does not contain infinity.

    • one year ago
  13. TuringTest Group Title
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    Infinity is a concept, not a number (I know I'm basically just restating, but it is worth emphasizing)

    • one year ago
  14. experimentX Group Title
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    you always write |dw:1349359774760:dw|

    • one year ago
  15. experimentX Group Title
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    you should have noted.

    • one year ago
  16. abdul_shabeer Group Title
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    then why 1/3 is considered a number?

    • one year ago
  17. TuringTest Group Title
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    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.

    • one year ago
  18. TuringTest Group Title
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    hm... I phrased that poorly :/

    • one year ago
  19. experimentX Group Title
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    natural number is defined as inductive set that begins with 1 and |dw:1349359861034:dw|

    • one year ago
  20. TuringTest Group Title
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    indeed what would 10000.....+1 be? could you write it? where would you put the 1 ?

    • one year ago
  21. abdul_shabeer Group Title
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    Why 0.333333333333333333....... is a number?

    • one year ago
  22. TuringTest Group Title
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    that is different from 0.3333....+1=1.3333... not problem there

    • one year ago
  23. experimentX Group Title
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    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.

    • one year ago
  24. TuringTest Group Title
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    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 ;)

    • one year ago
  25. TuringTest Group Title
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    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

    • one year ago
  26. chandhuru Group Title
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    @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 .......

    • one year ago
  27. abdul_shabeer Group Title
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    We can't locate 0.333333.......

    • one year ago
  28. TuringTest Group Title
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    yes we can

    • one year ago
  29. chandhuru Group Title
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    atleast u know that 0.33333 is present between 0.3 and 0.4 .... in case of infinity u cant ...... can u ????

    • one year ago
  30. TuringTest Group Title
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    |dw:1349360426152:dw|

    • one year ago
  31. TuringTest Group Title
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    now you show me what two numbers 1000..... lies between :)

    • one year ago
  32. abdul_shabeer Group Title
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    What is (0.333333......)* 10?

    • one year ago
  33. TuringTest Group Title
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    3.333333...

    • one year ago
  34. abdul_shabeer Group Title
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    0.333..... * 10 = 0.333...+0.3333....+0.3333....( 10 times) Can we add this?

    • one year ago
  35. TuringTest Group Title
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    I think it is a lot easier to see it as 1/3+1/3+1/3+...(ten times) =10/3

    • one year ago
  36. abdul_shabeer Group Title
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    I want to add it without converting it into 1/3

    • one year ago
  37. TuringTest Group Title
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    why?

    • one year ago
  38. abdul_shabeer Group Title
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    As 0.3333.... = 1/3, in whichever way i add I must get the same result

    • one year ago
  39. Razzputin Group Title
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    100000000000......... lies between 99999999999...... and 11000000000000...... where all three of the numbers stretch out infinitly.

    • one year ago
  40. TuringTest Group Title
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    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...

    • one year ago
  41. TuringTest Group Title
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    and @Razzputin that is wrong, how can you show me that 9999... is not bigger than 1000... ?

    • one year ago
  42. abdul_shabeer Group Title
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    How 0.999...+0.333...=1.222...?

    • one year ago
  43. TuringTest Group Title
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    are there more digits in one number or the other? no

    • one year ago
  44. Razzputin Group Title
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    what if you where to state that 999.... was 1 less than infinite?

    • one year ago
  45. TuringTest Group Title
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    ad a 3 to each 9

    • one year ago
  46. TuringTest Group Title
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    add*

    • one year ago
  47. TuringTest Group Title
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    oh my bad, .999.+.333...=1.333....

    • one year ago
  48. TuringTest Group Title
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    the 1's carry over

    • one year ago
  49. abdul_shabeer Group Title
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    |dw:1349364346874:dw|

    • one year ago
  50. abdul_shabeer Group Title
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    and the last digit would be 2

    • one year ago
  51. TuringTest Group Title
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    yeah but there are an infinite number of 3's and 9's so every digit carries a one from the previous decimal place

    • one year ago
  52. TuringTest Group Title
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    there is no last digit, that's why it's an infinitely repeating decimal

    • one year ago
  53. abdul_shabeer Group Title
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    There is no last digit, I just took a small value

    • one year ago
  54. TuringTest Group Title
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    which makes it not the same as 1/3+1 which is what you are trying to do

    • one year ago
  55. TuringTest Group Title
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    \[0.333\neq0.333...=1/3\]

    • one year ago
  56. TuringTest Group Title
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    this is why we don't add numbers with infinite decimals very often; It's ugly, confusing, and entirely unnecessary

    • one year ago
  57. abdul_shabeer Group Title
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    what do you get when you add 0.9999...+0.3333... without taking 0.99999...=1 and 0.333... = 1/3

    • one year ago
  58. TuringTest Group Title
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    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

    • one year ago
  59. TuringTest Group Title
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    at no point does the decimal terminate, hence EVERY digit carries a 1 from the digit after it

    • one year ago
  60. abdul_shabeer Group Title
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    But still you just can't neglect a 2

    • one year ago
  61. TuringTest Group Title
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    yes you can because there is absolutely no 2 how many decimal points down would you expect to find it?

    • one year ago
  62. abdul_shabeer Group Title
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    Which means it is not equal to 1+ 0.3333....

    • one year ago
  63. TuringTest Group Title
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    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

    • one year ago
  64. TuringTest Group Title
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    how do you figure that 0.999...+0.333... is not the same as 1+0.333... ?

    • one year ago
  65. abdul_shabeer Group Title
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    When we add, we add the numbers from Right hand side

    • one year ago
  66. TuringTest Group Title
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    so?

    • one year ago
  67. TuringTest Group Title
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    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?

    • one year ago
  68. TuringTest Group Title
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    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

    • one year ago
  69. abdul_shabeer Group Title
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    How do you add two numbers?

    • one year ago
  70. TuringTest Group Title
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    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

    • one year ago
  71. TuringTest Group Title
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    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

    • one year ago
  72. abdul_shabeer Group Title
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    0.9999.... = 1, I want to disprove this

    • one year ago
  73. TuringTest Group Title
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    you can't disprove something that is true

    • one year ago
  74. abdul_shabeer Group Title
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    Can you prove it?

    • one year ago
  75. TuringTest Group Title
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    again, what is 1-0.999... ?

    • one year ago
  76. TuringTest Group Title
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    prove it? yes would you like me to?

    • one year ago
  77. abdul_shabeer Group Title
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    yes

    • one year ago
  78. TuringTest Group Title
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    \[x=0.\overline9\]\[10x=9.\overline9\]\[10x-x=9x=9\]\[x=1\]

    • one year ago
  79. abdul_shabeer Group Title
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    0.999...*10 = 0.999...+0.999...+0.999...(10 times) How do you add this?

    • one year ago
  80. TuringTest Group Title
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    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...

    • one year ago
  81. abdul_shabeer Group Title
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    But what about the last digit. Though we don't get till last digit we observe that the last digit gets a different value

    • one year ago
  82. TuringTest Group Title
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    oh I did it with 0.333... but the idea is the same

    • one year ago
  83. TuringTest Group Title
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    where is this mythical last digit? what decimal place is it in? the tens, the thousands, the ten-millions?

    • one year ago
  84. TuringTest Group Title
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    what is the last digit of pi?

    • one year ago
  85. abdul_shabeer Group Title
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    It is an irrational number

    • one year ago
  86. TuringTest Group Title
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    but the point is the same, where is the last digit of 0.999... ? what decimal place is it in?

    • one year ago
  87. abdul_shabeer Group Title
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    How would you add 8467539+10384?

    • one year ago
  88. TuringTest Group Title
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    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*???

    • one year ago
  89. TuringTest Group Title
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    how can you start at the far right when there is no far right? you can't

    • one year ago
  90. abdul_shabeer Group Title
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    But you say that 0.3333..... is a rational number

    • one year ago
  91. TuringTest Group Title
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    yes and I can prove it what is your point?

    • one year ago
  92. abdul_shabeer Group Title
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    When you can't start at the far right, how do you take 0.999...*10 = 9.999...

    • one year ago
  93. TuringTest Group Title
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    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

    • one year ago
  94. abdul_shabeer Group Title
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    Why it is same as 1*10?

    • one year ago
  95. TuringTest Group Title
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    because 0.999...=1

    • one year ago
  96. abdul_shabeer Group Title
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    What is the standard way of adding two numbers?

    • one year ago
  97. abdul_shabeer Group Title
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    Not the grade school adding methods

    • one year ago
  98. TuringTest Group Title
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    brb @experimentX feel free to take over if you like I will be back in a sec

    • one year ago
  99. experimentX Group Title
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    i lost track of it ... looks like conversation reached almost infinity ... where do you have problem?

    • one year ago
  100. abdul_shabeer Group Title
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    What is the standard way of adding two numbers?

    • one year ago
  101. experimentX Group Title
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    think of addition as addition of distance.

    • one year ago
  102. abdul_shabeer Group Title
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    How would you add 8912394+1398124?

    • one year ago
  103. experimentX Group Title
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    draw a real line .. |dw:1349367528137:dw|

    • one year ago
  104. experimentX Group Title
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    |dw:1349367566686:dw|

    • one year ago
  105. abdul_shabeer Group Title
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    How would you add 0.999.... and 0.333...?

    • one year ago
  106. TuringTest Group Title
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    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

    • one year ago
  107. experimentX Group Title
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    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.

    • one year ago
  108. abdul_shabeer Group Title
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    This problem started in the proof of 0.999... = 1

    • one year ago
  109. experimentX Group Title
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    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

    • one year ago
  110. TuringTest Group Title
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    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

    • one year ago
  111. abdul_shabeer Group Title
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    Multiplication by 10 is nothing but adding it 10 times

    • one year ago
  112. experimentX Group Title
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    if you say this is 1 1.00000000000.. infinite zeros.....................1 then this must be equal to 1 too 0.99999999999999.... infinite nines

    • one year ago
  113. TuringTest Group Title
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    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

    • one year ago
  114. experimentX Group Title
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    I think you are misunderstanding infinity with undefined, infinity is greater than you imagine.

    • one year ago
  115. experimentX Group Title
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    1.00000000000.. infinite zeros.....................1 this means 1.00000000000.. here are more zeros than you imagine ....................1

    • one year ago
  116. TuringTest Group Title
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    @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

    • one year ago
  117. abdul_shabeer Group Title
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    You mean something which is at infinity is not there.

    • one year ago
  118. TuringTest Group Title
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    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

    • one year ago
  119. experimentX Group Title
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    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.

    • one year ago
  120. abdul_shabeer Group Title
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    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?

    • one year ago
  121. TuringTest Group Title
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    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

    • one year ago
  122. abdul_shabeer Group Title
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    if you are out of Milky way and you look at earth, would you be able to find it?

    • one year ago
  123. estudier Group Title
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    If it isn't 1 * 10^n, what is it?

    • one year ago
  124. TuringTest Group Title
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    with the right equipment, theoretically yes

    • one year ago
  125. abdul_shabeer Group Title
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    With no equipments

    • one year ago
  126. TuringTest Group Title
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    with the human eye (which is a piece of equipment itself in many respects)? no of course not, why does that matter?

    • one year ago
  127. abdul_shabeer Group Title
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    If we see the space out of earth, would it appear like a 2D image?

    • one year ago
  128. TuringTest Group Title
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    the ancients thought it was, so I guess you could argue yes, but that is just a matter of the limitations of human perception

    • one year ago
  129. TuringTest Group Title
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    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?

    • one year ago
  130. abdul_shabeer Group Title
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    Okay Thank You Max and ExperimentX

    • one year ago
  131. TuringTest Group Title
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    very welcome!

    • one year ago
  132. experimentX Group Title
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    no probs at all ...

    • one year ago
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