Does 1 = 0.999. . .?

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0=0.999 Math Science Numbers Proofs
valvin47
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    valvin47
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  • Added: 05-Dec-06

Some example proofs in the debate as to whether 1 is equivalent to the number 0. with an infinite number of 9s following the decimal. This debate is not yet settled, but take a look at the proofs to gain some insight. No audio.

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Does 1 = 0.999. . .?

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  • good examples

    the question of whether .9r = 1 is the same as does .3r = 1/3 ? Well, does it? The fact is that 1/3 doesn't even exist. If I have one, then by its very definition it is indivisible. But I can have 3/9, three ninths. This is reality that I am talking about. Mathematics describes reality. It is not reality.

    But in math, this is a limit problem. Just because a value is being approached does not mean that it is equal to it.

    By JPat 1165813243 Reply Spam Moderate Up Moderate Down
    • I agree

      I agree that we use math to describe reality, and should be careful not to confuse math with reality.

      Why is 1 indivisible? If I have 1 kilogram of a substance, is it impossible to divide it into 2 0.5 kilogram parts?

      Another argument against the proofs is that there should be an infinite number of points between 0.999... and 1. This alludes to the limit problem you mentioned.

      However, what number exists that is greater than .999.. but less than 1?

      By valvin47 1165876052 Reply Spam Moderate Up Moderate Down
    • also

      in the equation 1 - x = .999999r What is x? .0000000000000 where do we put the 1?

      oh yeah, i just remembered... i dont have time to look it up, but in studying binary numbers I learned that some rational decimals can be irrational binaries, and vise versa... so if a number is irrational such as .999, maybe it can be represented as a rational in another base.

      By JPat 1165876893 Reply Spam Moderate Up Moderate Down
    • 0,999 is rational

      (so 0,999.. too)

      By huncros 1193785964 Reply Spam Moderate Up Moderate Down
  • STUPID!!!!!!!!

    All of the equations offered as proof are all the same assertion of the statement. They are not different at all. They are all the same claim so let's take the first and you'll see how all the rest fall.
    1/3=.3|
    this is true but remember that the rounding off of the numbers is equal to less than half therefore if you round off you round DOWN!!!
    keep that in mind.
    Now do the multiples of 2 on each side.
    2*1/3=2*.3|
    2/3=.6|
    And this is nearly true but not absolutely because you still have the rounding up value..6667
    Next step, instead of 2 try 3 as the vid showed.
    3*1/3=3*.3|
    the 3's cancel, so:
    1=.9|
    Again, this is only true if you consider that you must round up first.
    ________
    In conclusion, stop putting into your mind what you are seeing which is 1=.9
    It is NOT 1=.9
    It is 1=.9|
    in other words, it is
    1=.9 rounded up.
    1=1
    Thank you.

    By reformedman 1166313453 Reply Spam [-1] Moderate Up Moderate Down
    • Clearly you don't understand

      There is no rounding involved here. This is a problem many people seem to have trouble with. Rounding is only used for convenience since in practice we can't keep an infinite number of places after a decimal point.

      In rounding, we intentionally truncate a number to something that is NOT equal to the real number, but close enough for our needs. So
      1/3=0.333... is true, but if we round to one decimal place we get
      1/3=0.3. However, 1/3 is NOT equal to .3, it is actually equal to 0.333... Try rounding at different places. If we round 1/3 to .3 and multiply by 100, we get 30. But if we round it to .33, we get 33. Clearly that shows that rounding only leaves us with an approximately equal number, not the real number.

      But in this case, there are an infinite number of 9s after the decimal place, and at no point do we have a final 9. The proofs show that such a number is equal to 1, without rounding.

      By valvin47 1166378519 Reply Spam Moderate Up Moderate Down
  • This is the classic math debate

    Its nothing new Valvin, how do keep making it to producer rewards. Its also funny that you should have posted this around the same time wikipedia did an expose on it. Hmmm me thinks that you have no original thought. BTW, if you think i believe for a second that you have a degree in physics and chemisty with a PHd in Chem coming (cereal packet maybe) then my little friend you are sadly mistaken.. I have a doctorate and im also next inline to be the president of the US.
    As for your video topic, you can choose either side of the fence on this topic just like the rest of the mathematical world. Its funny how both arguments can be right depending on whether or not you favour infintesimals or not.. peace

    By Monkeybitme 1169861064 Reply Spam [-2] Moderate Up Moderate Down
    • I never said this was new

      This video followed from a debate I had with several of my lab mates. I posted this to demonstrate in one place several of the proofs we discussed.

      Just because many people have seen and debated this doesn't make it any less interesting to people who will see it in the future.

      By valvin47 1169873480 Reply Spam Moderate Up Moderate Down
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