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.9 recurring = 1

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    #32
    sd123
    Closed Accounts Posts: 534 ✭✭✭sd123


    A number divided by itself is always 1, right.

    press the Pi button on a calculator. you should get 3.141592654. Now divide it by pi and you get 1. this is what we expect.

    now press pi/ 3.141592654. the answer you get is .9999999999.

    dunno how relivant this is but it is interesting nontheless. probably comes down to inaccuracies in the calculator itself


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    #33
    Professor_Fink
    Registered Users Posts: 861 ✭✭✭Professor_Fink


    sd123 wrote:
    now press pi/ 3.141592654. the answer you get is .9999999999.

    dunno how relivant this is but it is interesting nontheless. probably comes down to inaccuracies in the calculator itself

    Yes, it does. The number on the screen is not exactly the same as the internal representation of pi, so when you copy it down, and rekey it in, you introduce an inaccuracy.


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    #34
    sd123
    Closed Accounts Posts: 534 ✭✭✭sd123


    yes but if you key it in ie put 3.141592654/pi, it'll come up 1. but if you key in pi/3.141592654 you'll get .99999999999


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    #35
    bonkey
    Registered Users Posts: 15,443 ✭✭✭✭bonkey


    And if you put in .99999999999 and hit 1/x, what do you get?

    (If you're not using a scientific calculator, do 1 / .99999999999)

    Seriously...calculators are *not* comparable to proper mathematics. And no...for the record...computers aren't either.


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    #36
    Son Goku
    Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    Just to be more specific 0.999999............. is a way of representing the infinite sequence:

    9/10 + 9/100 + 9/1000 + 9/10000 + .....................

    Let's set this equal to some number s.

    9/10 + 9/100 + 9/1000 + 9/10000 + ..................... = s.

    Pull out a factor of 1/10:

    1/10 (9 + 9/10 + 9/100 + 9/1000 + ..........) = s

    However s = 9/10 + 9/100 + 9/1000 + ..........

    So this becomes:

    1/10(9 + s) = s

    Multiplying by 10

    9 + s = 10s
    9 = 9s
    1 = s = 9/10 + 9/100 + 9/1000 + .......... = 0.999999......

    I hope that proves it to people's satisfaction.

    N.B.
    Also remember infinity isn't a real number so expressions like (infinity - 1) are meaningless.


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    #37
    sd123
    Closed Accounts Posts: 534 ✭✭✭sd123


    N.B.Also remember infinity isn't a real number so expressions like (infinity - 1) are meaningless.

    That means that you just contradicted your own 'proof' :confused:


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    #38
    bleg
    Registered Users Posts: 5,848 ✭✭✭bleg


    people,people wikipedia is your friend

    and yes .99999... =1

    http://en.wikipedia.org/wiki/0.999...


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    #39
    bleg
    Registered Users Posts: 5,848 ✭✭✭bleg


    people,people wikipedia is your friend

    and yes .99999... =1

    http://en.wikipedia.org/wiki/0.999...


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    #40
    Pherekydes
    Registered Users Posts: 16,109 ✭✭✭✭Pherekydes


    sd123 wrote:
    That means that you just contradicted your own 'proof' :confused:


    eh? How?

    Are you getting confused between infinite and infinity?

    .9... is a real number. Infinity is not.


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    #41
    Son Goku
    Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    sd123 wrote:
    That means that you just contradicted your own 'proof' :confused:
    How so? I don't see where I did. Nowhere did I refer to a number called infinity and perform arithmetic on it.


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    #42
    Capt'n Midnight
    Moderators, Recreation & Hobbies Moderators, Science, Health & Environment Moderators, Technology & Internet Moderators Posts: 90,700 Mod ✭✭✭✭Capt'n Midnight


    since this thread is in science and not maths I can only assume you are refering to physical meanings

    there are only about 10^90 atoms in the observable universe +/- a coulple of orders of magnitude
    the number of different locations is when you divide a sphere of 15 billion light years diameter by the Planck Length
    the number of time intervals is the 15 billion years divided by the Planck time
    I don't know the smallest energy levels of photons, but electrons usually only jump between different band levels with specific energies, unless we are dealing with electron clouds

    Multiply that all together and express it as powers of powers and you could write it all down. More importantly the number of digits in the number would represent the number of 9's you need such that for all physical meaning it would .9 recurring would be the same as 1


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    #43
    sd123
    Closed Accounts Posts: 534 ✭✭✭sd123


    Son Goku wrote:
    How so? I don't see where I did. Nowhere did I refer to a number called infinity and perform arithmetic on it.

    The 's' you used above is a sum to invinity, therefore when you attempted to subtract numbers from it its a contradiction.


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    #44
    Son Goku
    Closed Accounts Posts: 1,475 ✭✭✭Son Goku


    The 's' you used above is a sum to invinity, therefore when you attempted to subtract numbers from it its a contradiction.
    When did I subtract from s?
    Also s is an "infinite series". There is no numerical quantity called inifinity that I manipulated.


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