What is .99 repeating as a fraction?
Quote: JyBrd0403The dart thrown at a dart board hitting Pi has a different problem. Pi is such a small number that it would be impossible to just hit Pi. The dart might hit Pi and 3.14 and 3.144 and 3.15 and 3.12 and 3.1234 etc. The point of the dart head would cover a ton of numbers ... in this "reality".
If you can imagine a dart being thrown at a dart board that has only one destination, that destination being Pi, what would have to happen for that dart to hit Pi? Somehow, the dartboard will have to become Infinitely big. It would have to grow to immense proportions for the dart to land on Pi. Probabilities of that happening are incredibly small, but (with no limits applied) there is a possibility of it happening. That is what would normally be called imagination.
The probability of the number picked being pi approaches zero, but is not zero. That's why I wouldn't make the bet. It means .000... != 0. .000... may have millions of values, but 0 has no value at all.
You're wrong on most of your assumptions, but your conclusion is correct (well...mostly)...
The size of the number has nothing to do with it. In fact, 3.14 and Pi are pretty close in "size"...(again, depending on what is "close)...The reason you would never hit Pi is because it is an irrational number, which means it can only be represented in decimal by an approximation.
The reason that the second instance is not impossible is because Pi is a number, between 3 and 4, and has an equal chance of being picked just like every other number between 3 and 4.
It would be the same if I said "Guess a number, any number" The probability of us guessing the same number is 0%, however it is not impossible.
Finally, 0 and every representation of 0 has the value 0. I'm not sure why you think that numbers are different because there is more or less precision given to them. Remember that part of third grade where the teacher taught you to divide and that one-half is the same as 0.5. Not sure why you are choosing to neglect this knowledge...
Quote: Wizardbut constraints in English betray explaining how something can have a 0% chance and still happen.
The English definition of zero is very well defined. It means the absence of value. So, if I bet 0% chance, it would equal "no chance" of winning at all. So, by English definition Zero = 0% = no chance of winning = zero chance of winning. Therefore,
If 0 = .000... I would WIN the bet.
If 0 != .000... I would LOSE the bet.
So, does 0 = .000... or does 0 != .000...
You gave me the answer, Wiz!
Quote: TriplellYou're wrong on most of your assumptions, but your conclusion is correct (well...mostly)...
The size of the number has nothing to do with it. In fact, 3.14 and Pi are pretty close in "size"...(again, depending on what is "close)...The reason you would never hit Pi is because it is an irrational number, which means it can only be represented in decimal by an approximation.
The reason that the second instance is not impossible is because Pi is a number, between 3 and 4, and has an equal chance of being picked just like every other number between 3 and 4.
Triplell, you leaped ahead again. "Pi is an irrational number" ... " Pi is a number" . "Pi can only be represented in decimal by an approximation". "Pi has an equal chance of being picked just like every other number".
You're contradicting yourself, Triplell.
In truth, Pi is a number cut off at a limit.
Quote: TriplellI'm not sure why you think that numbers are different because there is more or less precision given to them.
Triplell, it's because numbers ARE different because there is more or less VALUE (precision) given to them.
Quote: TriplellRemember that part of third grade where the teacher taught you to divide and that one-half is the same as 0.5. Not sure why you are choosing to neglect this knowledge...
I remember that part. I'm neglecting it because ... well .... simply ... it doesn't add to my arguement. :)
Quote: JyBrd0403Triplell, you leaped ahead again. "Pi is an irrational number" ... " Pi is a number" . "Pi can only be represented in decimal by an approximation". "Pi has an equal chance of being picked just like every other number".
You're contradicting yourself, Triplell.
In truth, Pi is a number cut off at a limit.
No. Pi is the ratio of diameter to radius of a circle.
Pi is NOT a number cut of to a limit. An approximation to pi is, but that is not pi.
The dart thing has nothing to do with the irrationality of numbers. There is an infinite number of rational values between thre and four as well as an infinite number of irrational numbers between three and four.
Quote: thecesspitNo. Pi is the ratio of diameter to radius of a circle.
Pi is NOT a number cut of to a limit. An approximation to pi is, but that is not pi.
Good point. I was going to say that .999... is 9's repeating to infinity, but not going past infinity. I just thought, that would be too confusing.
.999... is cut off at the limit of Infinity, but does not go past Infintiy? Confusing enough? If not, what's Infinity + Infinity ? The answer is Infinity. So, there's Millions of numbers between Infinity and Infinity?
I think it's better to cut the number off before Infinity.
You say, Pi is an approximation of Pi, but not Pi itself. That's like saying .999... = .999... but is not .999... itself. It doesn't make sense.
These numbers are cut off at the limit of the "highest known number available at the time".
Quote: JyBrd0403Good point. I was going to say that .999... is 9's repeating to infinity, but not going past infinity. I just thought, that would be too confusing.
.999... is cut off at the limit of Infinity, but does not go past Infintiy? Confusing enough? If not, what's Infinity + Infinity ? The answer is Infinity. So, there's Millions of numbers between Infinity and Infinity?
I think it's better to cut the number off before Infinity.
You say, Pi is an approximation of Pi, but not Pi itself. That's like saying .999... = .999... but is not .999... itself. It doesn't make sense.
I didnt say that though. I said an approximation to pi is not pi.
Quote:These numbers are cut off at the limit of the "highest known number available at the time".
No, they are not.
Quote: Nareed
Seriously, I am very attached to Aristotle's Law of Identity. So therefore 0.999... < > 1
What in the world does law of identity have to do with it??? Law of identity states that 1=1. You have to be a real master of sophism to manage to derive from it somehow that 1 <> (something else).
Quote: weaselmanWhat in the world does law of identity have to do with it??? Law of identity states that 1=1. You have to be a real master of sophism to manage to derive from it somehow that 1 <> (something else).
If A is A, then it is not something else. Therefore is 1=1, then 1 <> 5. Unless you claim 1=5
If 0.999... != 1, then what fraction is equivalent to 0.999... ?
Quote: TriplellSo all this talk of "leaping ahead" and skipping questions answered, I have one riddle.
If 0.999... != 1, then what fraction is equivalent to 0.999... ?
I gave you a fraction that equals 0.999... on page 23 of this thread.
Quote: NareedIf A is A, then it is not something else.
This may or may not be true, depending on what exactly you mean by "something else", and what you denote by A.
For example, a string "0.999..." is obviously not the same as "1". But both strings (albeit, different) refer to the same number.
Likewise, a letter A is obviously not the same as a letter B. But if both of them are used to reference the same thing (for example, number 1), then you can say, that A=B.
But in any event, it has nothing to do with law of identity. You cannot conclude that A != B from the fact that A=A. It could very well be that A=A and A=B.
Law of identity is the affirmation, that identical objects must be equal to each other. Logical reversal of that statement would be "unequal objects must not be identical", not "non0identical objects must be unequal", as you trying to make it. The latter is logically fallacious.
Quote:Therefore is 1=1, then 1 <> 5. Unless you claim 1=5
Right. But I do claim that 0.999... = 1.
Quote: weaselmanRight. But I do claim that 0.999... = 1.
He's got an equation that shows .999... = 1, Nareed. :)
Quote: JyBrd0403
If 0 != .000... I would LOSE the bet.
what the hell does 0 ! mean? LOL. I read it zero factorial and that = 1
Quote: edwardwhat the hell does 0 ! mean? LOL. I read it zero factorial and that = 1
!= means "Not equal to"
Quote: weaselmanThis may or may not be true, depending on what exactly you mean by "something else", and what you denote by A.
For example, a string "0.999..." is obviously not the same as "1". But both strings (albeit, different) refer to the same number.
Likewise, a letter A is obviously not the same as a letter B. But if both of them are used to reference the same thing (for example, number 1), then you can say, that A=B.
But in any event, it has nothing to do with law of identity. You cannot conclude that A != B from the fact that A=A. It could very well be that A=A and A=B.
Law of identity is the affirmation, that identical objects must be equal to each other. Logical reversal of that statement would be "unequal objects must not be identical", not "non0identical objects must be unequal", as you trying to make it. The latter is logically fallacious.
Right. But I do claim that 0.999... = 1.
FFS, we are talking about numbers here. Keep strings, ints, floats, characters, literals...whatever, out of it. The fact of the matter is that if someone says "I am 99.99 repeating percent sure"...then they might as well say they are 100% sure, because the numbers are the same...Which is what this thread is about...and it has been proved over and over (and at least in 10 different ways)...
Their seems to be only one person claiming otherwise, and his only argument is that "He came up with an equation" that shows when you plug in a number for x, that number still remains x after performing a series of operations. Congrats! That proves nothing.
On the other hand, if you perform completely valid operations on x, and at the bottom you get what appears to be a different value for x, then the values must not be different at all.
The funny part about all of it, is the fact that it doesn't matter. This man will go to his grave believing that 0.999... is not 1, and nothing will change his mind. Fortunately, there will never be a case in his life, where he is doing math, and he produces the number 0.999... or any other number that ends in x.xx999...
Thank god.
Quote: Triplell
Fortunately, there will never be a case in his life, where he is doing math, and he produces the number 0.999... or any other number that ends in x.xx999...
Well, maybe, not in his life, indeed, but people, familiar with basic math, stumble upon such cases quite regularly. Just multiply 1/3 by 3.
Now post after post I see where it's .999... is so close to 1 it doesn't matter, or a string of 9's is different then 1, or soft 1 vs hard 1. I'm just wondering when you're going to fold the hand?
If you concede that the 2 numbers have 2 different values, which everyone here has lately. It means they are 2 different numbers. For instance.
.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995
is a different number then
.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999996
2 different values = 2 different numbers.
Triplell, I would take a second look at the April 1 youtube post (She's Great). The operations may be valid, but the equation is invalid. Just like the operations for the equation showing all numbers are equal to each other are all valid operations, but the equation is invalid. So, all the equations showing .999...= 1 are all invalid. Reason being they show .999.... = 1 ! 2 different numbers can't hold the same value. 5 can't equal 6. 2 can't equal 1. Don't care what kind of math you do to come up with answer. Simple stuff.
Quote: weaselman
Likewise, a letter A is obviously not the same as a letter B. But if both of them are used to reference the same thing (for example, number 1), then you can say, that A=B.
You have 2 boxes box A and box B both have 1 pencil in them. Does box A = box B ? What if one box is big and one is small, one red one yellow. You get the point. So, we make both boxes identical and both pencils inside identical. Does box A = box B? If yes, are they the same box? Or, do you have 2 different boxes?
Quote: JyBrd0403You have 2 boxes box A and box B both have 1 pencil in them. Does box A = box B ?
What if one box is big and one is small, one red one yellow. You get the point. So, we make both boxes identical and both pencils inside identical. Does box A = box B? If yes, are they the same box? Or, do you have 2 different boxes?
First of all, "same", and "equal" is not the same thing. The boxes are indeed different. Weather or not they are equal to each other, depends on how you define equality in this case. If you define "=" as "contains the same number of pencils", then, indeed they are equal.
In case of "1", and "0.999...", it is a little bit different. It is actually the same number, expressed in two different ways, not two different numbers.
Quote: weaselmanFirst of all, "same", and "equal" is not the same thing. The boxes are indeed different. Weather or not they are equal to each other, depends on how you define equality in this case. If you define "=" as "contains the same number of pencils", then, indeed they are equal.
In case of "1", and "0.999...", it is a little bit different. It is actually the same number, expressed in two different ways, not two different numbers.
p
Number - An arithmetical value, expressed by a word or symbol, representing a particular quantity and used in counting, calculating, and for...
Note the word Particular
Particular - An individual item, as contrasted with a universal quality.
Note the word individual.
1 value = 1 number
2 different values = 2 different numbers
So, unless you're saying that .999... has EXACTLY the same value as 1 (note the Pi example), they're not actually the same number. If .999... is missing Pi, and 1 includes Pi, you have 2 differrent values.
Quote: Triplell
Their seems to be only one person claiming otherwise... This man will go to his grave believing that 0.999... is not 1, and nothing will change his mind. Fortunately, there will never be a case in his life, where he is doing math, and he produces the number 0.999... or any other number that ends in x.xx999...
Thank god.
All he is interested in doing is keeping the thread alive. If it lays dormant for a while, he comes in and posts to it repeatedly, over and over, until someone rises to the bait. It is the forum equivalent of banging on doors until someone answers.
153 of them have been to this thread. Of the 529 posts in this thread, the vast majority of them have been in reply to those 153. The initial question by MustangSally was discussed and answered by page 2 of the 53 pages.
38 posts were to a thread he started, discussing the number of trials to get 2/3/4 losses in a row flipping a coin. He started the thread, then argued with all the answers. Out of the total of 130 posts to the thread, the vast majority were in response to those arguments.
7 were to a thread he started, asking about how big a bankroll needed to back a D'alembert system. The thread totaled 19 posts. He tried to provoke an argument with leading questions, but no one took the bait and the thread petered out after 2 pages.
5 were to a probability question, out of a total of 15 posts to the thread. He made illogical arguments and argued the responses.
3 were to a roulette thread he started, out of a total of 7 posts to the thread.
2 were actually useful answers to the money/happiness poll.
1 was a laugh to a joke made by HotBlonde in the card counters/sense of humor thread.
I don't judge any of this, I simply present it as easily verifiable data.
Hey, that's a D'alemert on a 50/50 game of chance :)
33% of the time you win 2 in a row on a 50/50 game.
Thanks for not judging, Mosca.
Quote: MoscaI don't judge any of this, I simply present it as easily verifiable data.
In other words, he's the only 0.00000000000000000000000000...1 who disagrees that 0.9999999999999999999999... = 1
Quote: TriplellYes you would win.
One of my favorite math youtubers posted the following link recently, and I found it strangely ironic, but maybe it will help you :)
9.999... reasons that .999... = 1
And here is her April 1st post :)
Why every proof that .999... = 1 is Wrong
I really liked her math videos; I watched several of them. There was a lot of work and thought that went into each one.
Quote: JyBrd0403p
So, unless you're saying that .999... has EXACTLY the same value as 1
Yes, that is EXACTLY what I am saying.
Quote: JyBrd0403Sort of a slanted opinion of my postings don't you think? LOL.
Hey, that's a D'alemert on a 50/50 game of chance :)
33% of the time you win 2 in a row on a 50/50 game.
Thanks for not judging, Mosca.
It is what it is. I only did it as an exercise in data mining, I was curious because that is the only way you seem to engage people. I find the stamina remarkable. Not good, nor bad, but worth remarking on. So I remarked.
Quote: weaselmanYes, that is EXACTLY what I am saying.
How do you explain the Pi example? If 1 includes Pi and .999... does not include Pi. How is that the EXACT same value?
Quote: JyBrd0403How do you explain the Pi example? If 1 includes Pi and .999... does not include Pi. How is that the EXACT same value?
Who said that? "1 includes Pi and .999... does not include Pi" - is simply completely meaningless nonsense. You made that phrase up, and are now asking me to explain it. I can't. Because it's nonsense.
Quote: weaselmanWho said that? "1 includes Pi and .999... does not include Pi" - is simply completely meaningless nonsense. You made that phrase up, and are now asking me to explain it. I can't. Because it's nonsense.
Did you miss the Wizards Pi example. I changed it around for .999... but, if you had all the numbers between 3 and 4 in a hat you would have the value of 1. If you reach into the hat and pull out Pi, you would have .999... of the numbers between 3 and 4 left in the hat. That's the question I'm asking.
If 1 includes Pi and .999... does not include Pi. How is that the EXACT same value?
Change that to the probability of not choosing Pi , oh just look up the other posts. LOL.
All those numbers make up the value of 1. So, 1 includes Pi, and .999... does not include Pi. How is that the EXACT same value?
Quote: JyBrd0403I changed it around for .999...
Exactly. You changed it around to be nonsensical, and are now asking me to explain it. I cannot explain it, because what you are saying does not make any sense.
The probability of hitting Pi is 0. The probability of hitting any number including Pi is 1. The probability of hitting any number but Pi is 1 - (probability of hitting Pi) = 1.
Quote: weaselmanExactly. You changed it around to be nonsensical, and are now asking me to explain it. I cannot explain it, because what you are saying does not make any sense.
The probability of hitting Pi is 0. The probability of hitting any number including Pi is 1. The probability of hitting any number but Pi is 1 - (probability of hitting Pi) = 1.
So, your saying a hat filled with all the numbers between 3 and 4, and a Hat filled with all the numbers between 3 & 4 EXCEPT Pi, have EXACTLY the same value?
Quote: thecesspitInfinity - 1 = Infinity.
I agree with you. But, does the hat that has all the numbers between 3 & 4 and a hat that is missing Pi, have the EXACT same Value?
Note that .999... repeats to infinity. 1 does not. The 1st hat would represent 1. The second hat would represent .999...
Quote: JyBrd0403So, your saying a hat filled with all the numbers between 3 and 4, and a Hat filled with all the numbers between 3 & 4 EXCEPT Pi, have EXACTLY the same value?
I don't know what is the meaning of "value of a hat", or how you are able to imagine a "hat", containing an uncountable number of numbers. So, no, I am not saying that.
Quote: weaselmanI don't know what is the meaning of "value of a hat", or how you are able to imagine a "hat", containing an uncountable number of numbers. So, no, I am not saying that.
It's sorta like imagining .999... repeating to Infinity.
Quote: weaselmanI don't know what is the meaning of "value of a hat", or how you are able to imagine a "hat", containing an uncountable number of numbers. So, no, I am not saying that.
It's sorta like imagining .999... repeating to Infinity.
Are you trying to say that now you think that .999... does not exist?Quote: JyBrd0403It's sorta like imagining .999... repeating to Infinity.
Quote: JyBrd0403I agree with you. But, does the hat that has all the numbers between 3 & 4 and a hat that is missing Pi, have the EXACT same Value?
Note that .999... repeats to infinity. 1 does not. The 1st hat would represent 1. The second hat would represent .999...
The size (cardinality) of both those sets are exactly the same (aleph-1 if I recall my set theory correctly, but it might be aleph-0).
Quote: thecesspitThe size (cardinality) of both those sets are exactly the same (aleph-1 if I recall my set theory correctly, but it might be aleph-0).
aleph-0.999...
Next, you are saying that infinity - 1 = 0.999..., which is laughable.
Quote: TriplellThis is all pretty hilarious...You agree that infinity - 1 = infinity, but you disagree that if you take all the numbers between 3 and 4 (which is infinite) and you subtract 1 of them (pi), it no longer has the same value.
Next, you are saying that infinity - 1 = 0.999..., which is laughable.
Is it as laughable as someone saying 2 "numbers" have the same value. Or, am I still misreading it .999... isn't a number?
You want to know why an equation showing that all numbers are equal to each other is BS? It's not because the operations that were performed weren't valid, or because someone just decided to say that your not allowed to multiply by 0. It's because 2 numbers CAN'T share the SAME value. Period, that's it. Breaks the first rule of math. The equation is B.S. because the answers are nonsense, not because the operations were performed incorrectly.
You hold on to this .999... = 1 thing and it's ridiculous. .999... can only equal .999... 1 can only equal 1. Period. Any equation showing .999... = 1 is invalid, nonsense, not allowed, BS whatever you want to call it.
Could you please just answer one question that I can't get answered on this thread. What's the value of .333... and .666... ? Or, do they both equal 1 also? Maybe, they equal all other numbers, .333... could just equal 17, maybe .666... could equal 32.
Let me guess, .333... = .333... and .666... = .666... , but because you have an equation showing .999... = 1. .999... != .999... right?
you have been rehashing your argument endlessly.
why don't you move on to the next math argument.
you can choose to believe whatever you like about this topic,
nobody cares any more.
stick a fork in it. it's done
I just want to know if .333... =.333... or some other number.
Anyone know what the artifacts would be for base 9, which handles the 1/3 "problem" perfectly?
1/4 = .222...
2/4 = .444...
3/4 = .666...
OMFG, does .888... = 1.0
Or is someone going to argue that 1/4 in base 10 is not equal to .250... Or that .250... x 4 is not equal to 1.0... ??
Guess I have to take the limit of infinity into account for it all to make sense.
Quote: QuadDeucesSimple artifact of base 10. Nothing more, nothing less (aka equal).
Anyone know what the artifacts would be for base 9, which handles the 1/3 "problem" perfectly?
1/4 = .222...
2/4 = .444...
3/4 = .666...
OMFG, does .888... = 1.0
Or is someone going to argue that 1/4 in base 10 is not equal to .250... Or that .250... x 4 is not equal to 1.0... ??
Guess I have to take the limit of infinity into account for it all to make sense.
I'm actually pretty sure 1/4 isn't equal to .250... There's no repeating 0's there, there's no repeating 0's in 1.0 . No need, there's no 1 being carried out to limit of infinity. 1/4 = .25 Unless you want to tell me it actually equals another number?
You guys try real hard, and I'll bet you'll have every number equaling every other number in no time at all.
