0.99999~ = 1 ?

no matter how many nines you put you can still put another. Infinity is not a number. infinity is simply continuing without end. One can say there are are an infinite number of numbers between 0 and 1, since all numbers greater than 1 have a reciprocal that is between 0 and 1.

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There is no better love between 2 people than mutual respect for each other WT Young, 2002Who gave anyone the authority to call me an authority on anything. WT Young, 1969Since Evolution is only ~90% correct it should be thrown out and replaced by Creation which has even a lower % of correctness. W T Young, 2008

Huntard writes:

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What is it about math that makes people go mad, anyway? Or is it simply mad people that practice math?

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That's a question many have asked. You might want to pick up a copy of Logicomix which is about Russell, the development of the Principia, and an interesting study about the nature of looking into the void and having it look back at you.Russell's reaction to the foundations of mathematics was a bit different from Cantor, but Cantor was most likely bipolar.The interesting bit of Russell's background is that his parents were involved in a menage a trois and in the end, Russell seems to at the very least not minded his wife's affairs...until she had had two children by another man.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

Jon writes:

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I see no reason why Math could not permit such infinite divisions in contradiction to Reality, which clearly does not.

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You're still adding woo-woo where none exists.Let's try something simple: Repeat after me:0.999... is identical to 1.Can you say that with a straight face?

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

Jon writes:

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Care to explain?

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Let's see if I can provide an example of how infinite process still manage to complete.For this thought experiment, we need to make a few assumptions:1) You have an infinite number of coconuts in a pile, all numbered: 1, 2, 3, ....
2) You have a pit big enough to hold all of the coconuts (but they aren't in there.)
3) Superman and Captain Marvel both exist and can travel any distance in any length of time.Superman and Captain Marvel decide to play a game. At precisely 12:00 noon, Superman throws coconuts numbered 1 and 2 into the pit. Captain Marvel flies into the pit, grabs coconut #1, and throws it out of the pit.They sit around, having some coffee, talking about their adventures, and at 12:30 precisely, Superman throws coconuts numbered 3 and 4 into the pit. Captain Marvel flies into the pit, grabs coconut #2, and throws it out of the pit.Again, they sit around and socialize. At 12:45, in go coconuts 5 and 6, out comes 3. This continues, each time halving the amount of time they wait.Question: When 1:00 comes around, and 1:00 always comes around, how many coconuts are in the pit?The answer is: None. They all got thrown out. For every single coconut you care to name, I can give you an exact time when it was tossed out of the pit: Coconut #1 was tossed out at 12:00. Coconut #2 was tossed out at 12:30. #3 at 12:45, #4 at 12:52:30.So even though an infinite number of coconuts are involved, every single one of them was involved in the process and thus, not one is left in the pit when 1:00 comes around.This is why 0.999... is identical to 1: You ask how many 9s?All of them. Because we have all of them, 0.999... is not merely equal to 1, it is identical to it.And that's an even stronger statement.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

No matter how many coconuts were involved in the doings of the fractions of time 1:00, at exactly 1:00, Coconuts X and Y are taken to the pit by superman and Coconut Y is dutifully removed, at that exact fraction in time. (X+Y)-(Y)=X Coconuts in pit. (X+Y)=superman's contribution, (Y) equals Captain Marvels stolen booty and thus at any given fraction of time, assuming that Superman and marvel operate at exactly the same speed in that fraction, there will always be X-Y coconuts in the pit. the ONLY way that i could see a discrepancy is if X=0 and Y=1.Given:
1) Captain Marvel takes a coconut out for every 2 that superman deposits. At any given fraction of time, the result is always going to be 2-1. Right?

Let me try and think out loud about this hypothetical construct even more...(Math puzzles me, and i was never that good at it)This reminds me of the problem, (I forget the exact name) where the tortoise runs half as far as the hare....does anyone remember it?Given:1) Captain Marvel and Superman operate at the exact same speed.
2) Superman always deposits 2X as many coconuts in the pit as does Marvel take out.3) Time can be divided into infinitely small units of measure, and Superman and Marvel both can keep up the pace.Does it not then follow that for any given unit of time (T) there will always be 2 coconuts in and one coconut out? Thus, even if every single coconut can be accounted for by a number, there is always at that same moment a number twice as great going into the pit...thus at any given moment of time, X+X (or X+Y?) Coconuts are going into the pit, while either X or Y are coming out of the pit...leaving the contents of the pit always at some variable of X (or Y) be it 1X, 2X, google-X, or Infinity X.

Zeno's paradox that's called. The way I see it the problem is with the fact that there will be an infinite number of actions from both captain marvel and superman. given that there are an infinite number of times captain marvel will throw out a coconut, there will be no coconuts in the pit. the fact that superman throws in an infinite amount doesn't matter. In fact, maybe this helps: (superman's infinite coconuts) - (captain marvel's infinite coconuts) = 0Sounds logical to me, though it's probably completely wrong.

Phat responds to me:

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No matter how many coconuts were involved in the doings of the fractions of time 1:00, at exactly 1:00, Coconuts X and Y are taken to the pit by superman and Coconut Y is dutifully removed, at that exact fraction in time.

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Nope.This isn't about how many coconuts are in the pit before 1:00. This is about how many are in the pit at 1:00. Yes, you can calculate which coconuts are in the pit at any given time, but the ultimate question is what is the state of the system at 1:00, not before.1:00 always comes around. The universe does not sit and wait for us to make up our minds about what has happened.No matter what number you give me, I can give you a precise time that is before 1:00 when it comes out.If there were a coconut in the pit at 1:00, then it would have a number. But for every number you give me, I can tell you exactly when it left the pit, which was before 1:00.Therefore, the pit is empty.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

Phat writes:

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Captain Marvel and Superman operate at the exact same speed.

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Perhaps, but that isn't what was stated. Instead, the given is that Superman and Captain Marvel can move any distance in any time.

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Superman always deposits 2X as many coconuts in the pit as does Marvel take out.

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Indeed, but when you examine the problem, that isn't really that relevant. The heart of the question is: When do the coconuts come out? The problem is completely identical to this scenario:You have a pit filled with an infinite number of coconuts, all numbered. Assume Superman exists and can move any distance in any time. At 12:00, coconut #1 comes out. At 12:30, coconut #2 comes out. Coconut #3 comes out at 12:45, #4 at 12:52:30, etc.When 1:00 comes around, and 1:00 always comes around, how many coconuts are there in the pit?See, we've removed the entire "two go in" process and yet, the result is exactly the same and for the same reason: For every coconut you can name, I can tell you when it was removed from the pit, which was before 1:00. If there is a coconut in the pit at 1:00, then it has a number, but for every number, there is a time before 1:00 when it was removed.Therefore, the pit is empty.

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Time can be divided into infinitely small units of measure, and Superman and Marvel both can keep up the pace.

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That's the assumption mentioned above: They can travel any distance in any time.

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Does it not then follow that for any given unit of time (T) there will always be 2 coconuts in and one coconut out?

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Only in the sense that the scenario indicates that at each successive halving, Superman throws in two coconuts and Captain Marvel removes one. But that isn't the number of coconuts in the pit.At 12:00, there is one coconut in the pit: #2.At 12:30, there are two coconuts in the pit: #3 and #4.At 12:45 there are three coconuts in the pit: #4, #5, and #6.But this isn't about how many are in the pit before 1:00. It's about how many are in the pit at 1:00.And for every coconut, I can tell you exact when it was removed, which was before 1:00:#1 was removed at 12:00.#2 was removed at 12:30.#3 was removed at 12:45.It doesn't matter when the coconuts entered the pit. We can start with all the coconuts in the pit. The only thing that matters is when they leave.And they all leave before 1:00.Therefore, the pit is empty.

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Thus, even if every single coconut can be accounted for by a number, there is always at that same moment a number twice as great going into the pit...thus at any given moment of time, X+X (or X+Y?) Coconuts are going into the pit, while either X or Y are coming out of the pit...leaving the contents of the pit always at some variable of X (or Y) be it 1X, 2X, google-X, or Infinity X.

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Irrelevant. Start with all the coconuts in the pit.The only thing that matters is when the coconuts left. And they all left before 1:00.Therefore, the pit is empty.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

Huntard writes:

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(superman's infinite coconuts) - (captain marvel's infinite coconuts) = 0
Sounds logical to me, though it's probably completely wrong.

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No, you're right, but it isn't that simple. When I was first introduced to this question in my Advanced Calculus class, it was to point out part of the nature of infinity.The next day, Superman and Captain Marvel decide to alter the game:At 12:00, Captain Marvel throws in coconuts #1 and #2 and Superman flies in, grabs coconut #1, and tosses it out.After half an hour, at 12:30, Captain Marvel throws in #3 and #4, Superman flies in, grabs coconut #3, and tosses it out.After fifteen minutes, at 12:45, in go #5 and #6, out comes #5.When 1:00 comes around, and 1:00 always comes around, how many coconuts are in the pit?Easy: An infinite number. In this case, all the even ones.The moral of this story? Infinity doesn't play like normal numbers. Infinity - infinity is undefined. You need to explain what the infinity is in order to determine what the result is. The physical process of the first game and the second game are the same: Two go in and one comes out, but the result is different because what is coming out is not the same in both scenarios.As I mentioned to Phat, the description of the two going in is really a red herring. Start with all the coconuts in the pit. Then it becomes more clear what is going on: In the first case, all the coconuts are processed and thus, there are none left over.In the second case, only every other coconut is processed. And since the size of the odd numbers is the same as the size of the Natural numbers, even though you're processing the same number of coconuts, not all of them are touched and thus, there are some left over. An infinite number of them.We can adjust the process so that any arbitrary number of coconuts are left. Suppose that in the first scenario, Captain Marvel first throws out coconut #2, then #3 at 12:30, #4 at 12:45, and so on?When 1:00 comes around, there is exactly one coconut in the pit: #1.Infinity - infinity is undefined.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

What's also interesting is that in both cases, an infinite amount of coconuts have left the pit. Even when, in the second example, there is also an infinite amount left in the pit.Oh infinities, what fun they are to boggle the mind!

A quick thought from a mathematical ignoramus which might not be of much value.Could it be that the apparent contradictions in this sort of hypothetical arise simply because it's something that couldn't happen except in mathematical abstraction? There could never be an actual infinite number of coconuts, and time cannot be divided infinitely - Superman would still have an infinite number of coconuts to throw into the pit when there's only the Planck time remaining before 01:00.

Not at all. A set is infinite if and only if it is the same size as (i.e. can be put into a one-to-one correspondence with) a proper subset of itself.

You are confusing 2 different things, the number itself, which is finite, and the way we would write it down, which is infinite (but for the shorthand symbol |, fortunately).

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- xongsmith, 5.7d

Indeed. It is well understood by both y'all and myself that Reality is not infinitely divisible, which is why Zeno's paradoxes do not workat some point Achilles must move one whole unit, be it however small, because moving only 1/2 of that distance is not an option as the space it represents is not further divisible, and so he overtakes the tortoise.¹And herein lies the whole catch: an infinitely long string of 0.9999| represents what would be infinite divisibility (Message 173), which Reality does not permit. To check this, MATHSYSTEM introduces further rules to which Reality is not subject in order to mend the disconnect. Math having a rule which reality does not is part of the conventionalism that I discuss in the other thread.Please, correct me where I have erred. Jon
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[size=1]¹ In fact, Zeno starts his paradox arguments with the premise that space and time are infinitely divisible, notices his answers from such a premise are not in accord with Reality, and then should have concluded his assumptive premise on the infinite divisibility of space and time to be incorrect, which would mean space and time are not infinitely divisible but are made up of however small non-divisible wholes, which would have proven the Atomists had it right all along. BUT, I digress...[/size=1]Edited by Jon, : Link broken

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[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin