0.999…

This number read as .9 recurring is an interesting one. .9 recurring

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

It leaves me in awe…

If 0.999… = 1

Then what would 0.888… would be is it 0.9, it should not be coz 0.8999… = 0.9

and can 0.8(888…) can this be 0.89? if it is then what is the difference?

 

So is it 0.888… < 0.8999… < 0.9

 

So if we have a class of numbers lets say recurring terminating

0.888… < 0.888…5 < 0.888…5999… < 0.888…6 < 0.9 < 0.999…

 

This is just a vague idea, but probably we will never contemplate the outcomes of our understanding. This faintly reminds me of Gödel’s incompleteness theorems

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

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7 Responses to “0.999…”

  1. Ashok Says:

    Reminds me of the craziness of mathematicians… LOL.

  2. Usha Says:

    Fuzzy Logic Remember???

  3. sekhar muddana Says:

    Representation of real numbers using floating points is not UNIQUE, that is a number 1 can be represented both as 1.0 and 0.999999….. As far as mathematics is concerned there is ABSOLUTELY no difference among these two representations. There is a HUGE difference between terminating (or recurring blocks) and non-terminating floating point representations. Terminating (or recurring blocks) represent rational numbers (a proper subset of real numbers) and non-terminating numbers represent real numbers that are not rational (note that I am not calling them irrational). If anything this floating point represenation has some relavance to Cantor’s diagonalization and has nothing to do with Godel’s incompleteness.

  4. Simon Says:

    > If 0.999… = 1
    > Then what would 0.888… would be is it 0.9, it should not be coz
    > 0.8999… = 0.9

    No. 0.888… is equal to 8/9; i.e. 1 – 1/9.

    > So is it 0.888… 0.888… This is just a vague idea, but probably we will never contemplate the
    > outcomes of our understanding. This faintly reminds me of Gödel’s
    > incompleteness theorems

    …No. We know exactly the outcome of this. It has been understood, documented, recorded, and taught to first year Analysis I students for hundreds of years. And it has nothing to do with Godel’s theorems: Godel is about whether a set of axioms can ever be proven consistent, but that is irrelevent; if you take the set of axioms that comprise the real numbers and basic arithmetic, it is provable, unarguably, that 0.9 recurring is exactly and precisely equal to 1 in every possible way.

  5. vedil Says:

    I have written this not to prove/disprove anything mathematically, I am not good at mathematics anyways. but I see this as an intresting idea, and still people find it hard to accept 0.999… = 1 , although mathematically proved.
    So this is more like playing with words and getting fun out of it.

  6. Ashok Says:

    All Work and No Play Makes Jack a Dull Boy…

  7. Anand Verma Says:

    Why chess has only 64 squares?

    In how many years Sun will burn all its fuel?

    2 to the power 64

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