You are not logged in.
I'm frustratingly close to solving it. I've cracked the code, I've translated all the words, I'm just having trouble unscrambling the second-last phrase. Man that's annoying... :-p
I might've gotten it faster, but I didn't catch on to the box = word relationship until you posted the examples. From there it was real fast and easy to translate.
People don't understand what a manifold is or what it means to be homeomorphic.
Careful here! {ben} is a singleton in the powerset {P(people)}
Don't be silly, ben's not people! ben just thinks he's people. Ben's really a figment of my imagination. Sorry ben, I was going to tell you earlier but I just didn't have the heart to break it to you before now. ;-)
Infinte/Recurring 0.9 is a Number/Value But not a Fixed Number/Value! as with Whole Numbers!
Infinite/Recurring 0.9 = 0.(n) < 1 The 0.(n) is the Value from 1 - Infinite/Recurring 0.9 = 0.001...
So we can have 0.999... and 0.001... Where 0.999... + 0.001... = 1
I like how you always manage to completely avoid actually giving an answer to any direct question you're asked. Instead you just put a cut/paste of some irrelevant point you'd made 3 pages ago and leave it up to us to attempt to interpret how your "answer" has any impact on the question asked, and from there to guess at what it means you believe in relation to the actual question that was put forward.
In this case, I'm going to interpret the above to mean that you do indeed claim 0.999... isn't a real number. Unfortunately that interpretation leaves the rest of your post irrelevant, since we can't argue over what math does or doesn't make sense to perform on an unreal number, since no rules exist for that. So lacking any rules or any form of system to define what can and can't be done with an unreal number... hell, we're even lacking anything to call a "number" that's neither real nor complex... I'm forced to agree that whatever you put down there must make sense, since only you understand the "system" that you've apparently invented to deal with this peculiar case of an unreal number.
Or in other words:
0.6TG12bunnyrabbit + 63.523$omega23 = 2
Because in my system of unreal numbers that I choose to refer to as "hobos", I say so.
;-)
There is no Halfway! Concerning Infinity! But from Infinite/Recurring 0.9 ( Stage 0ne Decimal Place ) There will always be More 0.9's
So your argument is that 0.999... isn't a real number, then? Like I said above, this argument at least might have half a leg to stand on. Though then we can't prove any of the properties of this "number" using math, because normal math rules only apply to real numbers or complex numbers, and this doesn't seem to be either. So it's now basically just a digital representation of your ideal for a value less than (but almost equal to) 1. But still not a number, by conventional definitions of such.
Of course if you want to start arguing whether or not 0.999... is a real number then we'll just have to start from scratch with an entirely new set of arguments, and I can probably argue against that too... just saying... ;-)
Infinite 0.9 ( Stage One Decimal Place ) = 0.9
Infinite 0.9 ( Stage One Decimal Place ) + ( The Next Decimal Place " More 0.9's ) = 0.99
Infinite 0.9 ( Stage Infinite Decimal Place's ) = " More 0.9's " As always Before 1
But what number is halfway between "Infinite 0.9 (Stage Infinite Decimal Place's)" and 1?
There is only More 0.9's Between Infinite/Recurring 0.9 and 1
All you have to accept! is that there are Numbers Infinitly < 1
Can you show us one of these "more 0.9s" numbers?
0.999... has an infinite number of 9s. So you're asserting that there's another number bigger than 0.999... but less than 1, that has more than an infinite number of 9s? So to count from 0.999... to 1 ...
0.999... (infinite 9s)
0.999... (infinite +1 9s)
0.999... (infinite +2 9s)
...
0.999... (infinite + infinite 9s)
0.999... (2x infinite +1 9s)
0.999... (2x infinite +2 9s)
...
(etc, etc, etc)
Is this correct?
To Maelwys
Quote:" 0.999... / 2 = 0.5, because 0.999... = 1. ;-)
Or if you prefer
0.999... / 2 = 0.4999... (which incidentally, also = 0.5) "A.R.B
Wrong!!
0.9 / 2 " 1 Decimal Place " = 0.45
0.99 / 2 " 2 Decimal Place " = 0.495
0.9 Infinite Decimal Places / 2 " True Value can never be Calculated! "
0.4999... <> 0.5
Now you're just starting the exact same argument all over again with slightly different numbers. I understand that you refuse to believe that 0.999... = 1, and as such don't believe that 0.4999... = 0.5, nor 6.34999... = 6.35, but I don't think we need to argue every single case.
You still never answered my above question about the average of 0.999... and 1. If 0.999... is a real number < 1, then there must be another real number existing (x) where 0.999... < x < 1. The easiest such x to find should be simply the average of the two numbers that it's between. So what is that average? What is that number that exists between 0.999... and 1?
Or would you rather assert that 0.999... isn't a real number at all? That's something that you might at least make a case for. But if that's your case then you have to drop this nonsense that 1 - 0.999... = 0.000...1, because 0.000...1 isn't a real number either, and if we're starting to play with non-real numbers than we can't actually calculate anything because most of the normal rules of math cease to apply.
Some Doughnuts can be the Same Round Shape as an Apple!!
Yes, the entire "proof" clearly falls apart if you take timbits (doughnut holes, or whatever else you call them) into account. Even jelly-filled doughnuts would disrupt this proof! Clearly Poincaré wasn't thinking clearly and his entire work should be thrown out the window for these heinous oversights. ;-)
1 / 2 = 0.5
Infinite/Recurring 0.9 / 2 = ?
0.999... / 2 = 0.5, because 0.999... = 1. ;-)
Or if you prefer
0.999... / 2 = 0.4999... (which incidentally, also = 0.5)
Now for the the Wise Guys!
give us a Math Value (Decimal Places) for 1 and Infinite/Recurring 0.9
I'm not sure I undestand the question. You want to know how many digits follow the decimal place in each of those numbers? Well, 1 can have either 0 digits after the decimal (1) or infinite digits (1.000...). And 0.999... has infinite digits.
If you can Show how to Average an Unknown Number/Value Concerning Length and/or Decimal Places!
Its no Good just saying The average of Something is! "As far as Math goes! we need to know the Value as in Decimal Places! "
Did you even read my post, with lots of examples of how it IS possible to calculate the averages?
And remember, we're not dealing with unknown numbers here at all. We're dealing with infinitely long repeating decimals. Infinite doesn't mean "we don't know how many numbers follow because we can't count that high", it means "there's more numbers here than the largest finite (real or natural) number". You seem to be insisting on treating the "..." as "some more numbers follow, we don't know how many". If that was the case then yes, all of your arguments would be correct. There would indeed be a number that could add to 0.999(x more 9s) with a value of 0.000(x-1 more 0s)1 to make it equal 1. Though you'd still be able to calculate an average of 0.999(x more 9s)5 for it, but that's not a real number until we know the value of x. But the ... isn't an unknown variable, it's an unending number. There's definitely a difference here.
As far as I can tell, it's impossible. There are 24 (4!) possible solutions for which ball is which. Each weighing can result in 3 possible outcomes for that particular comparison (>, =, <). So even using the most efficient possible combinations to weigh, there's always a chance that there are two balls you don't know. To illustrate:
Start: 24 combinations. Define one test to perform, the solution is either > = or <. If you chose the most economic test, then this will narrow your possibilities down to 8 combinations. Again, choose the most economic test, and you'll either get > = or <. But breaking down 8 possibilities into 3 categories means that the number of possibilities per result is 2, 2, or 4. If you get a result with only 2 possible answers you can use the 3rd weighing to determine which of those answers is correct. If you get an answer that leaves 4 possibilities than your 3rd weighing will give you possible answers of < = or >, with possibilities per result of 1, 1, and 2. So there's a 50% chance here that you'll know the answer, but still a chance that you narrow it down to only two possible answers.
To further illustrate, here's a logic table for the first (or 3) branches of this test. The other two branches also have 3 possibilities, so they'll look very similar to this.
If AB < CD
If D < AB
If A < B
A = 1, B = 3, C = 4, D = 2
If A > B
A = 3, B = 1, C = 4, D = 2
If D = AB
If AC > BD
A = 2, B = 1, C = 4, D = 3
If AC = BD
A = 1, B = 2, C = 4, D = 3
**OR** A = 3, B = 1, C = 2, D = 4
If AC < BD
A = 1, B = 3, C = 2, D = 4
If D > AB
If A < B
A = 1, B = 2, C = 3, D = 4
If A > B
A = 2, B = 1, C = 3, D = 4
As you can see, there's one test in the middle that still leaves us with two possibilities. So it's not possible to answer 100% of the time, because in 1 test out of 8 (12.5% of the time) you'll need a 4th weighing to find the final answer.
1 / 0.3 = 0.333...
1 / 0.33 = 0.030...
And not 0.3 is the same as 0.3000....,
0.3 IS the same as 0.3000... though. I'm not sure what the above two calculations are supposed to prove, really.
Do you want more examples of averaging infinitely repeating numbers? I can even find the average of a repeating number with a non-repeating number. For example the average of 0.444... and 1 is 0.722(2)... The average of 1.232323(23)... and 5 is 3.0909(09).... The average of 1.5353(53)... and 2.361361(361)... is 1.9483574483574(483574)...
The moral of the story is that any two real numbers that have different values, also have a third real number with a unique value that is halfway between them, that represents the average of those two numbers. But for 1 and 0.999... there is no such value, which means that either 0.999... isn't a real number, or 0.999... has the same value as 1.
The fact that I have taken the Apple and the Doughnut as the Problem example! is no more foolish or Stupid than the original Statement below to Describe the Problem using of all things Rubber Bands?? (Thats also not Math? )
Yes, he's using apples, doughnuts, and rubber bands to simplify the problem. But what he's really discussing is the problem that when you bisec a sphere or a torus with a single line across the middle, it's possible to reduce the area of the section sliced by the line to a single point on a sphere, but not on a torus. But just because he uses one simplified method to explain doesn't mean that his example encapsulates every part of the original problem, or that his example can be examined and counterpointed as the only argument he has.
That's like if you said that 2 + 2 = 4 because I have 2 apples and you give me 2 apples, I'll have 4 apples. And then I could counter that by saying "No, 2 + 2 = 3, because one of those apples probably has a worm in it and then I'll just have to throw it out anyway, so it doesn't really count". You can only take an example to a certain point in math. ;-)
Alright, if you'll stick by your cop-out answer, that's fine for now. But it still doesn't answer:
4/ What is the average of 1 and 0.999...?
To Maelwys
A.R.B
You need to read Post #4
I did, and I think it's an extremely interesting conjecture. I just don't understand what the dough vs fruit properties of the two items have to do with the unique properties of their shapes (sphere vs torus)
To Maelys
Quote:" Okay. Using my understanding of the value of 0.999...,
1 / 0.999... = 1, because 0.999... = 1, and anything divided by 1 equals itself.A.R.B
How can a Number/Value ( 1 ) which is not Infinite/Recurring = a Number/Value that is (0.999...)
You're avoiding my question again. For the moment I'm not arguing that 1 and 0.999... do or don't equal each other. I'm just asking, based on your understand that 0.999... < 1, what is the result of 1 / 0.999...
It should be a fairly straightforward question, no?
To Maelwys
OK! you tell me 1 / Infinite/Recurring 0.9
Okay. Using my understanding of the value of 0.999...,
1 / 0.999... = 1, because 0.999... = 1, and anything divided by 1 equals itself.
But since you believe that 0.999... < 1, obviously this solution doesn't work for you, which is why I'm curious what you believe the answer would be to a question like that.
Okay, now that the other thread has apparantly been dematerialized, we can move discussion here.
I don't understand the point of your initial argument. Poincaré was discussing different properties of three dimensional shapes, specifically those that do or do not have simple meeting points (a sphere vs a torus) using the examples of an apple and a doughnut. You're simply comparing various other properties of an apple and a doughnut that are unimportant to the property being used in the proof, the basic shape. So how does your proof relate to Poincaré's work?
To Maelwys
1 Is not an Infinite/Recurring Number/Value! 1 has no ( repeating decimals! )
Infinite/Recurring 0.9 Is just one of Many Number/Values that are Infinitely < 1
You've repeated that anthem several dozen times already on this thread. Repeating it again, without any new context, doesn't add anything to your arguments. Can you please explain which of my above questions is this meant to address? And how it addresses the specific question? Thanks.
To Maelwys
You dont have to try and tell me what I have Posted! I should know Because I Know what Iv'e Posted!
All I meant to do was suggest that instead of duplicating posts, you should try to keep discussions to a single thread per discussion. If you believe that your thread is better placed on this board instead of the Jokes board, message one of the moderators, explain your reasoning, and ask him to move it. Simply reposting it against the moderator's move just breaks up discussion about the thread to two separate places, and causes clutter on two separate boards.
I believe you already posted this once, and it was moved to the Jokes forum. You should go look at thread there instead of re-posting it.
2/ What is the result of 1 divided by 0.999...?
2/ " You can't divide an Infinite Number into 1 Because no one Knows How long an Infinite Number is "
3/ What is the result of 2 divided by 0.999...?
3/ " You can't divide an Infinite Number into 2 Because no one Knows How long an Infinite Number is "
5/ What is the result of 0.999... multiplied by 0.999...?
5/ " You can't multiply an Infinite Number Because no one Knows How long an Infinite Number is "
6/ What is the result of 0.999... multiplied by 2?
6/ " You can't multiply an Infinite Number Because no one Knows How long an Infinite Number is "
Those all sound like cop-out answers to me. So 0.111... x 2 isn't 0.222...?
1/ What is the result of 1 minus 0.999...?
1/ 1 - 0.999... = 0.001...
For now I'll ignore that your ... doesn't make sense in that context (since it is generally accepted to represent continuing the same pattern for infinity, and your pattern seems to imply that the number is either 0.001001001001... or at least 0.00111111....
4/ What is the average of 1 and 0.999...?
4/ " The Average of 1 is 1 " " The Average of 0.9 is 0.9 "
I think you misunderstood the question. You can't have an average for each number seperately (well, okay you can... but it's stupidly obvious), I'm asking what the average of the two numbers is. The average of 1 and 3 is 2. The average of 1 and 2 is 1.5. What is the average of 1 and 0.999...? (basically, what is the number halfway between them)
-----------------------------------------------------------------------------------------------------------------
THE POINCARE CONJECTURE PROOF - By Me 12/06/07
-----------------------------------------------------------------------------------------------------------------
Problem = " How Can you Distinguish an Apple IIe from a Doughnut "
.....................................................................................................................................
The Poincare Conjecture Truth Table
.....................................................................................................................................
APPLE : DOUGHNUT
.....................................................................................................................................
IS IT A FRUIT No : No
.....................................................................................................................................
HAS IT MADE LOTS OF DOUGH Yes : Yes
.....................................................................................................................................
DOES IT GROW ON A TREE No : No
.....................................................................................................................................
IS IT MADE BY HUMANS Yes : Yes
.....................................................................................................................................
The Above Poincare Conjecture Truth Table,shows clearly that there is no difference between an Apple and a Doughnut!
;-)