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# .99999 repeating = 1?

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Look at it from this way;

Using mathematical rules we can deduec

Infinity. Infentily small must be 1/Infinity.

If 9.9 going to infinity is infinitly close to 1

Hence 1-9.999999etc = 1/Infinty

we know 1/Infinity = 0

hence 1-9.99999=0 hence 9.999999=1, its not nice, but deal with it, life isnt perfect.

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Er, right. That above post just didn't make sense.

Also, please note that infinity is not a number. It's a concept.

I have half a mind to go around and delete posts that make use of such "facts" that 1/infinity = 0. It's not right and it doesn't really have any meaning at all.

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Actualy, Dave, 1/0=infinity in both the extended reals, which aren't very interesting, and the one point compactification of the complex plane, aka the riemann sphere, which is very widely used in mathematics, especially complex analysis: it's automorphisms (in the proper sense) are the mobius maps, which are essentially SU(2). It is easy to show that any riemann surface that is locally euclidean is a quotient space of this sphere by some finite group action, and this tells us that hyperbolic geometry is the proper geometry of mathematics.

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Surely 1/0 = infinity could be rearranged to show that 1/infinity = 0 ?

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Actualy, Dave, 1/0=infinity in both the extended reals, which aren't very interesting, and the one point compactification of the complex plane, aka the riemann sphere, which is very widely used in mathematics, especially complex analysis: it's automorphisms (in the proper sense) are the mobius maps, which are essentially SU(2). It is easy to show that any riemann surface that is locally euclidean is a quotient space of this sphere by some finite group action, and this tells us that hyperbolic geometry is the proper geometry of mathematics.

That might be (I certainly didn't know that), but the majority of posts that we get around here containing infinity aren't used in the proper context. Maybe I'm just being picky, I don't know.

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I have half a mind to go around and delete posts that make use of such "facts" that 1/infinity = 0. It's not right and it doesn't really have any meaning at all.
Erm... damn. :/ I was under the impression that just as one could multiply by zero but not divide by it, that one could divide by infinity but not multiply by it.

I'm beginning to think that the only valid proofs of the whole 0.999 repeating = 1 thing are those which make a point to leave infinity out, and tend to be difficult to understand by those without a background in mathematics.

If I may ask one thing, matt grime: would you mind explaining the last line in your proof in post #23 in simpler terms if possible? (Then |x_n-y_n| = 10^{-n} hence in the reals, which is the completion of the rationals wrt euclidean distance, the limits are equivalent.) I can follow the proof up to this point but I'm just not sure how the result shows that they are equivalent. If not I'll just grab a book and check for myself, but others might be wondering too, and your proof seems the best I've seen so far.

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Well, the reals by one of the standard DEFINITIONS is the completion of the rationals in the euclidean norm. So this "step" follows trivially, in the mathematical sense. Ie two two sequences are declared to be equivalent if their difference is a sequence that tends to zero.

There are othere ways of giving a model for the real numbers, but they are all models of a totally ordered complete field, and any such is unique up to (unique) isomorphism, hence they are called the real numbers.

Remember, decimals are just representations of real numbers, they are not in any sense "actually real numbers".

And, Dave, yes, most people are misusing the notions of infinity, however, if you state they are doing something that is just plain wrong, one of them will come back with spaces where infinity is a member. None of these is the real numbers though.

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So if ive got £10,999,999,999,ive really got £11,000,000,000.Somehow it seems illogical 0.999=1,

We know from primary school that another integer is required.

Why all the maths to 0.999=1

When its 0.999+0.001=1

I believe that using the equations in this topic as is,will not yield a correct formula for calculating distance in regards to our universe.Math is fine as it is without leaving out integers.

no, .999999999 doesnt equal zero

.999999 repeating does.

you seem to have forgotten the infinite after the .999......

So think about it. .33333333 repeating equals 1/3

1/3 times 3 equals one.

.33333333 repeating equals .9999999 repeating

therefore, .9999999 repeating = 1

..in theory..

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you can't do that because .1111111111111111infinity isnt 1/9 it approaches it, but it never is actually 1/9

The proof with the x=.99999

10x=9.999

I dont believe that you can multiply something with infinite numbers by ten, because it would almost be like adding a number, a number would just appear....for some reason it just seems illogical.

Yes i agree it seems illogical. but all these formulas add up . and sure you can add something with infinite numbers by ten.

just imagine

setting it up like you set up any multiplication problem

10

.9

9

so therefore

10

.99

9.9

and...

10

.999

9.99

and so on...(which would be 9.9999 infinite)

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It's been 30 years since I took a university math course so please forgive my lack of coherent math expresion so well put by many postings above.

if .999 repeating equals 1

then does

8.99 repeating equal 9 ?

does .0199 repeating equal 02 and thus:

.99 repeating equals 1 and

does .011199 repeating equal 0112?

Then every interger and decimal in between repeated equal the next higher or lower number if it has a repeating 9?

and thus if a equals b and b equals c etc. then

Does every number equal every other number?

If this posting makes no sense that's fine but if it 'sort of' makes sense then a math keener might rephrase the intent. My skin is thick on this one and I defer to others.

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...if .999 repeating equals 1 then does 8.99 repeating equal 9 ?

8.999... = 8 + 0.999... = 8+1 = 9. A similar reasoning goes for your other examples.

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Please can we close this thread and the other ones on this question, it's come up many times, been proven, there's no use in repeating everything ad nauseum.

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This thread is two years old, anyway.

Closed.

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so what, I still dont buy into it either.

0.99999999... repeating is Never 1.

its always going to be 0.9999... blah blah blah repeating!

so Ner:-p

/me slaps YT.

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