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  • 1.9999… = 2
  • funkynick
    Full Member

    Discuss…

    😀

    Well, as we seem to be on a bit of a maths trip today…

    Posted 15 years ago
    5thElefant
    Free Member

    Wait until the economists see it. I’m sure they can come up with 1250 = 2.

    Posted 15 years ago
    clubber
    Free Member

    Untrue. Rounding is just an appoximation for convenience of writing/typing.

    Posted 15 years ago
    thisisnotaspoon
    Free Member

    depends on the question

    1.9999 does not equal 2, but does round up to it at 1,2,3 and 4 significant figures

    however if the question was:
    lim (x->0) 2-x = 2

    then yes the answer is 2.

    Posted 15 years ago
    Gary_M
    Free Member

    As above, it doesn’t equal 2 it’s rounded up to 2.

    Posted 15 years ago
    djglover
    Free Member

    2.49 = 2

    1.51 = 2

    Posted 15 years ago
    matthewjb
    Free Member

    If you mean 1.9999.. with the 9s going on forever then that does equal 2.

    Posted 15 years ago
    funkynick
    Full Member

    Well.. I meant it as a recurring.. that’s what the dots were for… unlike those ones which are meant to be an elipsis, but I can’t remember what the alt+code is for them.

    Posted 15 years ago
    glenh
    Free Member

    Surely 1.99 recurring approaches 2, but does not equal it.

    Posted 15 years ago
    Ewan
    Free Member

    1.9 recuring equates to 2.

    Same as 1/2 + 1/4 + 1/8 + 1/16 etc is equal to 1.

    Posted 15 years ago
    IanMunro
    Free Member

    1/3 = 0.333 recuring
    2/3 = 0.666…
    3/3 = 0.999…
    4/3 = 1.333…
    5/3 = 1.666…
    6/3 = 1.999…

    Posted 15 years ago
    Ewan
    Free Member

    Oh dear. http://en.wikipedia.org/wiki/0.999…

    Posted 15 years ago
    simonfbarnes
    Free Member

    1.9 recuring equates to 2.

    well, as a number you can write down 1.99999…. is always going to be less, as you cannot write an infinite number of 9s. And if you’re going to be merely conceptual, then they’re obviously different.

    The integers and the real number field are different things. If someone asks, “How many people are in the room?”, the answer cannot have a fractional part, even if one person has a missing leg. Integers count, real numbers measure.

    Posted 15 years ago
    Ewan
    Free Member

    Recurring means ‘a real number in the decimal numeral system in which a sequence of digits repeats infinitely’.

    Therefore 1.9 recurring does equate to 2. If you could write it down, it wouldn’t be recurring. Unless you had infinite time and resources.

    What have integers got to do with anything…? If you’re bothered by the above proof, replace ‘1’ with ‘1.0’.

    Posted 15 years ago
    GreenK
    Free Member

    But 10x – x cannot be 9x because x is not 1.0

    Posted 15 years ago
    nickc
    Full Member

    Yes they are exactly the same number

    Posted 15 years ago
    colande
    Free Member

    GreenK – Member

    But 10x – x cannot be 9x because x is not 1.0

    agreed 10x-x does not equal 9x
    edit; hang on im confused
    2nd edit; im totally down with you ewan now 😀
    that pickles my brain though

    Posted 15 years ago
    tyger
    Free Member

    Just while I’m working this out can someone remind me how the puzzle goes about 3 chaps who each pay £10 for something and there’s a discount and it should be £9 each and a £1 goes missing – or something like that?? Cheers

    Posted 15 years ago
    colande
    Free Member

    was it an english-man, irish-man and a scots-man type of joke???? 🙂

    Posted 15 years ago
    funkynick
    Full Member

    Of course 10x – x = 9x

    If I have ten x’s and remove one x, I have nine x’s… how is that not correct? It’s simple algebra surely…

    Posted 15 years ago
    tyger
    Free Member

    Yeah but…someone gives some change and it doesn’t add up ??

    Posted 15 years ago
    funkynick
    Full Member

    Right…

    Three men go to a hotel and pay the bellboy £10 each for a room for the night. The bellboy then takes the money down to the manager to pay, but the manager says it’s only £25 for the room tonight and gives the bellboy £5 to take back to the men.

    He takes the change back to the men, who tell him to give them each £1 and take £2 as a tip, so they each have paid £9 for the room.

    But, and this is the problem, if they have each paid £9 for the room, plus the £2 for the bellboy, when you add it all together you get £27 + £2 = £29… when they originally pay £30… so where has the extra £1 gone?

    Or something like that…

    Posted 15 years ago
    5thElefant
    Free Member

    Have you looked down the back of the sofa?

    Posted 15 years ago
    funkynick
    Full Member

    I found a pen and some sweets, but no money…

    Posted 15 years ago
    GrahamS
    Full Member

    Ah the joys of infinity.

    It’s a bit like claiming that the distance between any two points is infinite because the distance can be halved an infinite number of times.

    Posted 15 years ago
    tyger
    Free Member

    Many thanks! 🙂

    Posted 15 years ago
    colande
    Free Member

    the scots-man, did you check his pockets??????

    Posted 15 years ago
    colande
    Free Member

    also what are 3 men doing in one hotel room???

    Posted 15 years ago
    Cooroo
    Free Member

    1.9 recurring = 2, by definition I think!
    I love infinity. I’m off to read up on Hilbert’s hotel.

    Posted 15 years ago
    matthewjb
    Free Member

    if they have each paid £9 for the room, plus the £2 for the bellboy, when you add it all together you get £27 + £2 = £29… when they originally pay £30… so where has the extra £1 gone?

    That’s just adding when you should be taking away though.

    £9 each = £27

    £2 for the bellboy and £25 for the room =£27

    What missing £1?

    Posted 15 years ago
    thepurist
    Full Member

    If we’re talking infinity, are there more fractions or decimal numbers – and can you prove it?

    Posted 15 years ago
    jahwomble
    Free Member

    Assuming infinitely good eyesight,the required level of fine motor control and a precisely defined enough cutting tool, Occam’s razor may be good here.

    can you cut a piece of titanium (for example) exactly 1.9 recurring cms long? no you cant.

    can you cut a piece of titanium (for example) exactly 2.0 recurring cms long? yes you can
    .
    so no ,regardless of what Bertrand Russell and other assorted philosophical mit mots think, they are not exactly the same number at all, they may however be functionally identical numbers, unless the definition you need in your calculation is massively high.

    Posted 15 years ago
    IanMunro
    Free Member

    can you cut a piece of titanium (for example) exactly 1.9 recurring cms long? no you cant.
    Rather depends on what your dial is marked in. Mine’s mark at 120 degree intervals. So 3 marks per revolution, giving me settings (assuming infinitely good eyesight) of 1/3, 2/3 and 3/3. Now it’s indeniably that 1/3= 0.333…, 2/ =0.666…, 3/3=0.999… etc. So 2.0 turns of my dial yields a 1.999.. cut.

    Posted 15 years ago
    matthewjb
    Free Member

    If we’re talking infinity, are there more fractions or decimal numbers

    Decimals I think

    – and can you prove it?

    No it’s a long time since I did any serious pure maths

    Posted 15 years ago
    tommytowtruck
    Full Member

    Ah, good old William of Occam! Or Ockham?

    Posted 15 years ago
    captain_spaulding
    Free Member

    http://uk.youtube.com/watch?v=Bomv-6CJSfM

    Posted 15 years ago
    miketually
    Free Member

    Well.. I meant it as a recurring.. that’s what the dots were for… unlike those ones which are meant to be an elipsis, but I can’t remember what the alt+code is for them.

    alt+0133 (using the number pad)

    Posted 15 years ago
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