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abdul_shabeer

  • 2 years ago

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

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  1. KaylaBrewington
    • 2 years ago
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    yes because the number line never stops

  2. sauravshakya
    • 2 years ago
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    |dw:1349359330358:dw| Is infinity a number?

  3. experimentX
    • 2 years ago
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    not a natural number and not real number either.

  4. chandhuru
    • 2 years ago
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    infinity is something which cant be defined...

  5. experimentX
    • 2 years ago
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    no .. irrational number is a real number.

  6. abdul_shabeer
    • 2 years ago
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    Is it a number?

  7. sauravshakya
    • 2 years ago
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    IS infinity a number?

  8. experimentX
    • 2 years ago
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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.

  9. experimentX
    • 2 years ago
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    *in

  10. sauravshakya
    • 2 years ago
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    If 100000000000000... is not a natural number then the set of natural number is finite. right?

  11. chandhuru
    • 2 years ago
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    @experimentX how do u say that it is not a real number??

  12. experimentX
    • 2 years ago
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    no ... the set of natural number is infinite but does not contain infinity.

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

  14. experimentX
    • 2 years ago
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    you always write |dw:1349359774760:dw|

  15. experimentX
    • 2 years ago
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    you should have noted.

  16. abdul_shabeer
    • 2 years ago
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    then why 1/3 is considered a number?

  17. TuringTest
    • 2 years ago
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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.

  18. TuringTest
    • 2 years ago
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    hm... I phrased that poorly :/

  19. experimentX
    • 2 years ago
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    natural number is defined as inductive set that begins with 1 and |dw:1349359861034:dw|

  20. TuringTest
    • 2 years ago
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    indeed what would 10000.....+1 be? could you write it? where would you put the 1 ?

  21. abdul_shabeer
    • 2 years ago
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    Why 0.333333333333333333....... is a number?

  22. TuringTest
    • 2 years ago
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    that is different from 0.3333....+1=1.3333... not problem there

  23. experimentX
    • 2 years ago
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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.

  24. TuringTest
    • 2 years ago
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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 ;)

  25. TuringTest
    • 2 years ago
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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

  26. chandhuru
    • 2 years ago
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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 .......

  27. abdul_shabeer
    • 2 years ago
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    We can't locate 0.333333.......

  28. TuringTest
    • 2 years ago
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    yes we can

  29. chandhuru
    • 2 years ago
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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 ????

  30. TuringTest
    • 2 years ago
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    |dw:1349360426152:dw|

  31. TuringTest
    • 2 years ago
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    now you show me what two numbers 1000..... lies between :)

  32. abdul_shabeer
    • 2 years ago
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    What is (0.333333......)* 10?

  33. TuringTest
    • 2 years ago
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    3.333333...

  34. abdul_shabeer
    • 2 years ago
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    0.333..... * 10 = 0.333...+0.3333....+0.3333....( 10 times) Can we add this?

  35. TuringTest
    • 2 years ago
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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

  36. abdul_shabeer
    • 2 years ago
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    I want to add it without converting it into 1/3

  37. TuringTest
    • 2 years ago
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    why?

  38. abdul_shabeer
    • 2 years ago
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    As 0.3333.... = 1/3, in whichever way i add I must get the same result

  39. Razzputin
    • 2 years ago
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    100000000000......... lies between 99999999999...... and 11000000000000...... where all three of the numbers stretch out infinitly.

  40. TuringTest
    • 2 years ago
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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...

  41. TuringTest
    • 2 years ago
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    and @Razzputin that is wrong, how can you show me that 9999... is not bigger than 1000... ?

  42. abdul_shabeer
    • 2 years ago
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    How 0.999...+0.333...=1.222...?

  43. TuringTest
    • 2 years ago
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    are there more digits in one number or the other? no

  44. Razzputin
    • 2 years ago
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    what if you where to state that 999.... was 1 less than infinite?

  45. TuringTest
    • 2 years ago
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    ad a 3 to each 9

  46. TuringTest
    • 2 years ago
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    add*

  47. TuringTest
    • 2 years ago
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    oh my bad, .999.+.333...=1.333....

  48. TuringTest
    • 2 years ago
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    the 1's carry over

  49. abdul_shabeer
    • 2 years ago
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    |dw:1349364346874:dw|

  50. abdul_shabeer
    • 2 years ago
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    and the last digit would be 2

  51. TuringTest
    • 2 years ago
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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

  52. TuringTest
    • 2 years ago
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    there is no last digit, that's why it's an infinitely repeating decimal

  53. abdul_shabeer
    • 2 years ago
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    There is no last digit, I just took a small value

  54. TuringTest
    • 2 years ago
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    which makes it not the same as 1/3+1 which is what you are trying to do

  55. TuringTest
    • 2 years ago
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    \[0.333\neq0.333...=1/3\]

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

  57. abdul_shabeer
    • 2 years ago
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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

  58. TuringTest
    • 2 years ago
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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

  59. TuringTest
    • 2 years ago
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    at no point does the decimal terminate, hence EVERY digit carries a 1 from the digit after it

  60. abdul_shabeer
    • 2 years ago
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    But still you just can't neglect a 2

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

  62. abdul_shabeer
    • 2 years ago
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    Which means it is not equal to 1+ 0.3333....

  63. TuringTest
    • 2 years ago
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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

  64. TuringTest
    • 2 years ago
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    how do you figure that 0.999...+0.333... is not the same as 1+0.333... ?

  65. abdul_shabeer
    • 2 years ago
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    When we add, we add the numbers from Right hand side

  66. TuringTest
    • 2 years ago
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    so?

  67. TuringTest
    • 2 years ago
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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?

  68. TuringTest
    • 2 years ago
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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

  69. abdul_shabeer
    • 2 years ago
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    How do you add two numbers?

  70. TuringTest
    • 2 years ago
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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

  71. TuringTest
    • 2 years ago
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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

  72. abdul_shabeer
    • 2 years ago
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    0.9999.... = 1, I want to disprove this

  73. TuringTest
    • 2 years ago
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    you can't disprove something that is true

  74. abdul_shabeer
    • 2 years ago
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    Can you prove it?

  75. TuringTest
    • 2 years ago
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    again, what is 1-0.999... ?

  76. TuringTest
    • 2 years ago
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    prove it? yes would you like me to?

  77. abdul_shabeer
    • 2 years ago
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    yes

  78. TuringTest
    • 2 years ago
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    \[x=0.\overline9\]\[10x=9.\overline9\]\[10x-x=9x=9\]\[x=1\]

  79. abdul_shabeer
    • 2 years ago
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    0.999...*10 = 0.999...+0.999...+0.999...(10 times) How do you add this?

  80. TuringTest
    • 2 years ago
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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...

  81. abdul_shabeer
    • 2 years ago
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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

  82. TuringTest
    • 2 years ago
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    oh I did it with 0.333... but the idea is the same

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

  84. TuringTest
    • 2 years ago
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    what is the last digit of pi?

  85. abdul_shabeer
    • 2 years ago
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    It is an irrational number

  86. TuringTest
    • 2 years ago
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    but the point is the same, where is the last digit of 0.999... ? what decimal place is it in?

  87. abdul_shabeer
    • 2 years ago
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    How would you add 8467539+10384?

  88. TuringTest
    • 2 years ago
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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*???

  89. TuringTest
    • 2 years ago
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    how can you start at the far right when there is no far right? you can't

  90. abdul_shabeer
    • 2 years ago
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    But you say that 0.3333..... is a rational number

  91. TuringTest
    • 2 years ago
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    yes and I can prove it what is your point?

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

  93. TuringTest
    • 2 years ago
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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

  94. abdul_shabeer
    • 2 years ago
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    Why it is same as 1*10?

  95. TuringTest
    • 2 years ago
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    because 0.999...=1

  96. abdul_shabeer
    • 2 years ago
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    What is the standard way of adding two numbers?

  97. abdul_shabeer
    • 2 years ago
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    Not the grade school adding methods

  98. TuringTest
    • 2 years ago
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    brb @experimentX feel free to take over if you like I will be back in a sec

  99. experimentX
    • 2 years ago
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    i lost track of it ... looks like conversation reached almost infinity ... where do you have problem?

  100. abdul_shabeer
    • 2 years ago
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    What is the standard way of adding two numbers?

  101. experimentX
    • 2 years ago
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    think of addition as addition of distance.

  102. abdul_shabeer
    • 2 years ago
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    How would you add 8912394+1398124?

  103. experimentX
    • 2 years ago
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    draw a real line .. |dw:1349367528137:dw|

  104. experimentX
    • 2 years ago
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    |dw:1349367566686:dw|

  105. abdul_shabeer
    • 2 years ago
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    How would you add 0.999.... and 0.333...?

  106. TuringTest
    • 2 years ago
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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

  107. experimentX
    • 2 years ago
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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.

  108. abdul_shabeer
    • 2 years ago
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    This problem started in the proof of 0.999... = 1

  109. experimentX
    • 2 years ago
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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

  110. TuringTest
    • 2 years ago
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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

  111. abdul_shabeer
    • 2 years ago
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    Multiplication by 10 is nothing but adding it 10 times

  112. experimentX
    • 2 years ago
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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

  113. TuringTest
    • 2 years ago
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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

  114. experimentX
    • 2 years ago
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    I think you are misunderstanding infinity with undefined, infinity is greater than you imagine.

  115. experimentX
    • 2 years ago
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    1.00000000000.. infinite zeros.....................1 this means 1.00000000000.. here are more zeros than you imagine ....................1

  116. TuringTest
    • 2 years ago
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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

  117. abdul_shabeer
    • 2 years ago
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    You mean something which is at infinity is not there.

  118. TuringTest
    • 2 years ago
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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

  119. experimentX
    • 2 years ago
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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.

  120. abdul_shabeer
    • 2 years ago
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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?

  121. TuringTest
    • 2 years ago
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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

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

  123. estudier
    • 2 years ago
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    If it isn't 1 * 10^n, what is it?

  124. TuringTest
    • 2 years ago
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    with the right equipment, theoretically yes

  125. abdul_shabeer
    • 2 years ago
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    With no equipments

  126. TuringTest
    • 2 years ago
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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?

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

  128. TuringTest
    • 2 years ago
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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

  129. TuringTest
    • 2 years ago
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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?

  130. abdul_shabeer
    • 2 years ago
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    Okay Thank You Max and ExperimentX

  131. TuringTest
    • 2 years ago
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    very welcome!

  132. experimentX
    • 2 years ago
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    no probs at all ...

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