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posted April 07, 2005 10:42 AM Profile for Ryan McGuire Send New Private Message Edit/Delete Post Reply With Quote Just to reopen the original can of worms...
Concerning .999(9) == 1...
 Do we all agree that the proofs given so far are sufficient?
 Have there been counterproofs?
 Are people still unconvinced but unable to explain why?
 Somthing else?
I tried to make that list unbiased to either the They're Equal or They're Unequal camps, but since I count myself as being on the Equal side of the fence (to mix my metaphors with a 9.999(9) foot pole), I may have failed.
Originally posted by James Christian:
So not only are we making up names for non existant numbers but we are also giving them both negative and positive values.
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population."  Chetan Parekh
Originally posted by James Christian:
I'll try and make it easy to understand. If I have five oranges and I divide them among 5 people each person gets 1. If I divide them among 2 people each person gets 2 and 1 is left over. Optionally of course they could break the remainder in half but that's beside the point. If I divide the 5 oranges between 0 people the 5 oranges remain 5 oranges. They are not divided into an infinite number of infinitely small pieces and shared out to nobody. Hence, scientifically 5/0 = 0 remainder 5 not infinity remainder 0.
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population."  Chetan Parekh
There are only two hard things in computer science: cache invalidation, naming things, and offbyone errors
Originally posted by James Christian:
Is there a smallest number larger than 0? If so what is it?
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population."  Chetan Parekh
Originally posted by James Christian:
BUT if you were to ask me would 0.999(9) pass the (0.999(9) instanceof 1) test then the answer would be certainly NOOOO!!!
The reason being 1 is a number that exists and 0.999(9) is a fictitious concept that helps people get their phd's when there is nothing left to study that helps mankind. :roll:
"I'm not back."  Bill Harding, Twister
Originally posted by Steven Bell:
I suppose PI would also be considered a fictitious concept. We should ban any and all numbers that don't end!
Stupid math people making life so darn difficult for the rest of us. Who do they think they are anyways.
Originally posted by Jim Yingst:
The limit is zero.
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population."  Chetan Parekh
"I'm not back."  Bill Harding, Twister
I suppose PI would also be considered a fictitious concept. We should ban any and all numbers that don't end!
It can readily be shown that the irrational numbers are precisely those numbers whose expansion in any given base (decimal, binary, etc) never ends and never enters a periodic pattern
I've heard it takes forever to grow a woman from the ground
"I'm not back."  Bill Harding, Twister
posted April 09, 2005 02:04 PM Profile for Nick George Email Nick George Send New Private Message Edit/Delete Post Reply With Quote James, you and your hypothetical, abstract models! Who's ever heard of an orange that can neither be eaten nor decompose? You can make all the abstract models you like, but in the real world you eat your orang
Is the value of 1/3 infinite?
Is the value (not representation) of 0.333(3)... infinite?
If you say it's infinite  could we at least agree it's somewhere greater than 0 and less than 1? Does that not mean it has finite limits?
Regarding pi: are you saying you think it's possible we will one day discover that pi has an exact nonrepeating decimal representation? (Presumably, a really long one, but not infinitely long?)
Are you going so far as to say that such a representation must exist (because pi is "finite") even if we don't know exactly what it is?
I've heard it takes forever to grow a woman from the ground
Originally posted by James Christian:
If we further this argument we obtain interesting results.
However using base 12 as has been seen 1/3 = 0.4 and 0.4 * 3 = 1, no problems. BUT the closest number to 1 in base 12, which if does exist should be equal to our mythical 0.999(9) in base 10. However, in base 12 our mythical number is 0.bbb(b) and only at a far stretch of the imagination could 0.4 * 3 equal 0.bbb(b) in base 12 whereas 0.444(4) * 3 could theoretically fulfill the relationship. Translating 0.444(4) into base 10 we arrive at a value which is greater than 0.333(3). Hence our mythical 0.999(9) when divided by 3 give two different values. Does that seem mathematically acceptable to anybody?
"I'm not back."  Bill Harding, Twister
I've heard it takes forever to grow a woman from the ground
Does that seem mathematically acceptable to anybody?
It works just fine of you do the math right.
posted April 09, 2005 10:23 PM

I know you're not a big fan of proofs, but for what it's worth to you,
Proof that Pi is irrational

whereas 0.444(4) * 3 could theoretically fulfill the relationship.
Only if you think (as Warren alludes) that 4 * 3 = 11, or b in duodecimal. I'd think 0.444(4) * 3 would equal .ccc(c) (since 4 * 3 is 12, not 11( except of course all those c's are too big for duodecimal, and each c would beome 10 in doudicimal, carrying over to yield a result of 1.111(1). Yeah, I know using the c temporarily was a bit unorthodox, but at least I got the right result.
But, come to think of it, all the proofs listed here so far have fallen by the wayside.
Originally posted by James Christian:
But the question still remains with what do we divide 1 to obtain 0.999(9)
and for them matter to obtain 0.000(0)1 and furthermore seeing as the basic unit in each base has a different magnitude after the decimal point (i.e 0.1 > 0x0.1) is not 0.000(0)...1 greater than 0x0.000(0)...1 .
If the smallest number greater than 0 does exist and it expresses the difference between 1 and 0.999(9) (which we have seen = 1), how can the smallest number greater than 0 have two different values in two different bases?
Surely by now we must be unanimous that the smallest number greater than 0 does not exist as there will always be a number smaller than it.
Originally posted by Gerald Davis:
Ask me this if you was to give a child a card with a number 0 plus infinite number of 9 cards and told him to lay out the 9 cards until all the nine cards magically disappear and the 0 turns into a 1, he will most likely to say that will never happen even if infinity is reachable.
Something that is infinite cannot equal something that is finite like an integer or float number.
For instance: If you divide up a pie into 9 pieces, you could say each piece is "1/9" of the original. Or it might be "0.111(1)" of the originial. Or it might be "0.1 (base 9)" of the original. The fact that in base 10 the piece of pie has a repeating representation while in base 9 it has a terminating representation doesn't change the piece itself; it's still just one ninth of the pie.
However, the same cannot be said for 0.999(9) as nobody has any difficulty in reading and understanding 1. In fact the only time we see 0.999(9) mathematically is when we do an operation similar to the following with a calculator:
And this is only due to the fact that the calculator, due its limitations, has lost that certain something that makes 1/3 ever so slightly larger than 0.333 .
Is there a smallest number greater than 0?
If so is this the greatest number lesser than 0.1? 0.0999(9)
And this 4.999(9)? Does that equal 5?
And finally what about this? 7.1000(0)1 Is this the smallest number greater than 7.1?
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