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0.999r=1? Discuss

freddemillio	Date: August 11, 2005 @ 2:18 PM "It is also to remember that there are two kinds of infinities: Countable Infinities and Non-countable Infinities. The set of whole numbers is a countable infinity. The set of bumbers between 0 and 1 is a non-countable infinity." I have to stop typing with my nose. That should read: It is also important to remember that there are two kinds of infinities: Countable Infinities and Non-countable Infinities. The set of whole numbers is a countable infinity. The set of numbers between 0 and 1 is a non-countable infinity. The infinity of numbers between 0 and 1 is bigger than the infinity of whole numbers. (Maybe it made more sense with bumbers . )
evansorchid	Date: August 11, 2005 @ 2:35 PM One infinity can be bigger than another infinity? Now I am hopelessly lost.
freddemillio	Date: August 11, 2005 @ 2:44 PM Here is a link that explains some of the concepts between countable and non-countable infinities. In particular it discusses Cantor's diagonal proof which is an interesting way to try to get a handle on the concept. http://en.wikipedia.org/wiki/Cantors_Diagonal_argument
Snoogans775	Date: August 11, 2005 @ 5:50 PM hey, since it wasn't confusing enough,, why don't we put it into MARTRIX FORM, what the hell is wrong with you CANTER!
Intergalacti...	Date: August 11, 2005 @ 7:45 PM if 2.5 plus 2.5 equals five does _ _ that mean 2.49 plus 2.49= 5 or less than five?
kingo	Date: August 11, 2005 @ 9:26 PM 2.49... + 2.49... = 5.0 (them thar dot dot dot things mean the previous digit is repeating, in this case, cuz them thar lines over the 9s like you intended don't really show up over the 9s.) Any decimal terminating in a string of repeating 9s somewhere after the decimal point is equal to what you'd get if you round the decimal to the place before the 9s start. So 2.49... = 2.5, and 2.29... = 2.3, and 490848.3434349... = 490848.343435
GeneHilbert	Date: August 11, 2005 @ 10:39 PM I buy gas @ 2.299 per gallon and I buy 20 gallons that = 45.999998 but the pump reads $46.00. I’m not seeing an infinite, only an absolute here... Why?... Get over the corporate greed factor... I'm not getting some theoretical equation - I'm receiving hard rounded math. Again, get over it ...... Why? Could this be a conundrum? I think not. Hard math or theory…. hmmm? Economics, theory, interpretation or mathematical absolutes...... hmmm..? A mathematician I’m am not - that was my great, great, Uncle David Hilbert’s gig. I am just a lowly guitar player. Although I know there is no such thing as a constant - only variables and similarities. So if mathematical theory is your strong suit - I am truly impressed and salute you - you have my utmost admiration. I do well to make 1, 8 and 15 work unitarily... but ultimately make sure you can pay the water bill and balance your bank accounts.
zedsalt	Date: August 12, 2005 @ 12:24 PM Using the marks of ellipsis instead of _r makes sense as replacement for putting a _ over a number. I'll start doing that, too. I'm told that ! before an = means not equal. Is that right? Or would that just be confusing matters further? Anyhoo, you'll notice that among the folks that used the 1/3=.3... as a proof that .9...=1, no one ever stated that 1/3+1/3+1/3=.9... or that .3...+.3...+.3...=1. The first one would just be silly, right? 1/3+1/3+1/3 easily resolves into a tidy 1. I think everyone's reluctant to use the second equation because its left side never really resolves. If they were to say that adding three infinites to each other ever resolved into a finite quantity, that would be arbitrarily choosing a point at which to stop adding threes to each other, and the equation just doesn't provide for that. What makes anyone willing to do the EXACT same thing by stating that .9...=1?
kingo	Date: August 12, 2005 @ 1:38 PM Serious confusion here. .3... is not an "infinite." It's just a repeating decimal. Because we are saying that the 3s repeat infinitely does NOT mean this value is somehow "unresolved" or that it's an "infinite." It is, very straightforwardly and simply, the decimal representation of 1/3. 1/3 MEANS 1 divided by 3. 1 divided by 3 is .3... You can come to that conclusion by doing the math, long division-wise. I wish I could write out the long division here, but message boards don't do that well. So do it by hand if you have a chance. What that means is that writing 1/3 + 1/3 + 1/3 IS EXACTLY THE SAME THING as writing .3... + .3... + .3... And that's precisely why the proof mux originally offered works. As you just said, 1/3 + 1/3 + 1/3 works out quite tidily to 1. .3... + .3... + .3... works out quite tidily to .9... And that means 1 = .9...
Snoogans775	Date: August 12, 2005 @ 2:24 PM I like that the best as well.
wailingmiserere	Date: August 12, 2005 @ 3:07 PM Zed, one of the reasons why people wouldn't usually write: 1/3 + 1/3 + 1/3 = 0.9...., or 0.3... + 0.3... + 0.3... = 1 is because they are two different notation systems. It's like writing the same melody in different clefs, to use a musical example. One system uses fractions, the other uses decimals. 0.9... is a decimal representation of 1. Like if you wanted to write the A above middle C in the bass clef, you'd have to use ledger lines, which would be a little inconvenient, but unavoidable in certain cirumstances. It's still the same note (or number) but just notated differently.
pog	Date: August 13, 2005 @ 2:06 AM ...More like Stevie Vai coming up with the 16 note octave
Cowboy666	Date: August 13, 2005 @ 2:37 AM Never quite made it to 1. Just hanging around .9r myself is good enough for me. Too much pressure being 1!
zedsalt	Date: August 13, 2005 @ 12:18 PM But these syntactic issues ultimately fail in proving the equation. "Saying that a digit repeats infintely is NOT the same as saying it infinitely repeats". Um...o.k....if I applied that logic, I can see how saying that a number is less than one is NOT the same as saying that it isn't equal to one. I could say it; I just couldn't believe it. To clarify an earlier post: Hendrik Antoon Lorentz and James Clerk Maxwell were physicists. Maxwell was a Scot, which makes Ron's funny German mispronunciation even funnier. He can recite and explain over a half-dozen of Maxwell's theories, but JCM's nationality had apparently slipped Ron's mind. In his own defense, Ron said that Maxwell usually went by just "Clerk Maxwell", and somebody ELSE'S lame attempt at a Scottish accent had likely "thrown" him. The "Blavatski" he mentioned was "Madame Blavatsky", the theosophist Elena Petrovna Blavatskaya. "I was looking for a name to attach to all of the world's major religions...they all rely upon a value existing between point nine to infinity and one...and I figured Theosophy was the way to go. I was going to say 'Joseph Campbell', but I think Madame Blavatsky was more 'into' math. To be fair, I should've mentioned the same number of mathematicians, physicists, and religious scholars. So, add Riemann [mathematician Georg Friedrich Bernhard Riemann] and Ouspensky [theosophist Peter Demianovich Ouspensky] to my list, because all mathematics, physics, and religion relies on the existence of a quantity between point nine to infinity and one."
evansorchid	Date: August 13, 2005 @ 2:25 PM
zedsalt	Date: August 13, 2005 @ 2:26 PM this just in: "I visited the web site [page] we've been discussing, and I have something I'd like to add. There's nothing to invalidate 1/2=.5 as an equation. In fact, it's the more common type of equation: that which equates a process...a fraction is by definition a process...to a perfect expression of the result of that process. The other type of valid equation is that which equates a process to another process which results in the same perfect expression of the same quantity. What invalidates 'point nine to infinity equals one' as an equation is that both point nine to infinity and one are...Mr. McCollough?" "Quantities?" That's right, Mr. McCollough, quantities".
kingo	Date: August 13, 2005 @ 7:33 PM Dude. wtf? That is the biggest piece of gibberish I've ever seen. And I KNOW gibberish. Who's this coming from, exactly? There is no such... whatever that thing is... in math that "invalidates" an equation because both sides of the equals sign are quantities. 1 = 1 is not an invalid equation. .9... = 1 is NOT an invalid equation. There's nothing semantic about this, unless you consider that the language of math is all semantic. The fact that you aren't willing to accept the logic of a mathematical proof only means that you're disregarding the validity of mathematics. And if that's what ya wanna do, then by all means, be my guest. And furthermore, to re-arrange what you just quoted, which was gibberish, in order to make a valid equation which FITS the random definition of equations that someone pulled out of thin-air, or at least pulled out of somewhere that's not been sourced here: 1/1 = .9... 1/1 is exactly as much a "process" as 1/2 is. But backing up a step... 1/2 is a fraction. Which is a quantity. So is .5, because THEY'RE THE SAME DAMN THING. Neither is more or less process than the other.
zedsalt	Date: August 14, 2005 @ 11:56 AM Ron Smith. I reached him through his wife, who occasionally employs the services of my mother at the Marshall County Historical Society Museum. "There is no such... whatever that thing is... in math that "invalidates" an equation because both sides of the equals sign are quantities. 1 = 1 is not an invalid equation." EXACTLY!!! The one on the left is a quantity. The one on the right is the same quantity. One quantity is not "quantities". "1/1 is exactly as much a "process" as 1/2 is." EXACTLY!!! There's no difference between saying "one divided by two" and saying "one half". ".5" on the other hand...we all know what process "/" represents what process are you saying a decimal point represents?
kingo	Date: August 14, 2005 @ 1:14 PM Unfortunately I seem constitutionally unable to stop having this discussion... It's really not even an argument; I don't know why I keep arguing it. All I can say is that Ron Smith, whoever he is, is speaking of something that's not really math, at least not the kind I know. You're not really making sense because you're using definitions that don't really mean anything. An equation has nothing to do with a "process." Your statement here REALLY says it all: "The one on the left is a quantity. The one on the right is the same quantity." THAT is a perfectly acceptable definition of an equation. The thing on the left side of the equal sign is the same as the thing on the right side of the equal sign. This is why mathematical proofs WORK. And you're not accepting that. When I say 1 = .9..., the EXACT THING I'M SAYING is that: "The one on the left is a quantity. The one on the right is the same quantity." THEY ARE THE SAME QUANTITY. Mathematical proofs WORK THIS WAY. You are arguing against that fact, and so if this argument can get anywhere you need to tell me what type of logic you're using that says that the following set of equations has a logical flaw: 1/3 = .3... (technically this is an identity; it's simply showing the conversion of the fraction 1/3 to its decimal representation, .3...) Then we can multiply both sides of this equation, or identity, by 3; we can do this according to the multiplication property of equality (if a = b, then a * c = b * c) so we have: 3 x 1/3 = 3 x .3... simplified, this looks like: 3/3 = .9... To simplify the left side further, we can divide the numerator and the denomiator of 3/3 by 3, which gives us 1/1, so: 1/1 = .9... simplify the left side further and we have: 1 = .9... There is no logical flaw in this set of equations. You can't argue against it unless you explain where the flaw is; and if you're going to come up with a flaw that's based on some definition of equation that's not the standard mathematical one, you're going to have to show me the source for that definition.
Intergalacti...	Date: August 15, 2005 @ 8:14 AM Isn't a definition an meaning of somethin though. How can you define somethin if nothin really means that one thing? Just thought I'd throw a spanner in the works
zedsalt	Date: August 15, 2005 @ 11:47 AM If .3... is a perfect representation of 1/3, mankind will NEVER, EVER...no matter how hard we try...be able to invent a machine that can cut a pizza into three equal slices.
kingo	Date: August 15, 2005 @ 11:50 AM that's as it should be. When 3 pieces are required, just cut the thing into halves, then I'll take a half. Then cut the remaining half in half again and the other two people can have those two pieces. QED
wailingmiserere	Date: August 15, 2005 @ 12:02 PM If you're talking about dividing something circular into threes, then you'd do it in degrees... 120 degrees for each slice.
wailingmiserere	Date: August 15, 2005 @ 12:03 PM Although Halaka's way sounds much more sensible from a mathematical standpoint
Intergalacti...	Date: August 15, 2005 @ 12:07 PM hehe wail just wailed on everyone there
desiderata	Date: August 15, 2005 @ 5:11 PM I bought a ukulele. Got that a UKULELE? It plays infinitely awesome songs that are all based around repeating digits that are the equivalent of their equivalent fractions in a given set of pizza pies. If I had a potato right now, I'm fairly certain it would explode. Stop this madness now! Oh, and genocide. Stop the genocide too.
Intergalacti...	Date: August 15, 2005 @ 5:31 PM hehe
pog	Date: September 9, 2005 @ 8:20 PM This thread is still bugging me. If you multiply 0.3... (infinitely reocurring, aka 1/3) by 3, you will get 1, but if you multiply 0.3 (no reocurring numbers, just 0.3) by 3, you will get 0.9 See how they aren't the same thing? You will only ever get 0.9... (reocurring) from the first instance if you get a machine to try and explain 1/3 in a decimal format, and machines are not perfect enough for this task because they have limitations. When they manage to invent a calculator with unlimited memory capacity, then they'll be able to represent an infinite reocurrance, and then it would take forever to calculate !?!?
Intergalacti...	Date: September 9, 2005 @ 8:32 PM Dicscuss 28 plus7 =0
kingo	Date: September 10, 2005 @ 12:25 AM Pog I'm gonna kick you in the nuts.
pog	Date: September 16, 2005 @ 6:04 AM Okay.... I've had enough fun with this. I hope no one got too ticked off by it all, as I can't help it if it intesests me. To be honest, I have 2 schools of thought on this topic. I seriously believe both to be theoretically possible. Both seem feasible, but you can also believe one, both or none of these 2 submissions. So here goes. The best way to explain both theories is not to look at the reocurring numbers, but to look at the distance (or measurable amount) between 1 and 0.9... for example, if 0.9... was indeed a finite number or amound of reocurring digits such as 0.999 then the distance between it and 1 would be 0.001. Again if the number was 0.99999, the difference would be 0.00001 and so on. Now, this bring me to my 2 most feasable concepts.... the one that a lot of you guys believe (and I don't believe I ever said it was wrong. In fact most mathmaticians pass this off as the most logical theory) is that if you truly had an infinite number of 9's in 0.999... then the distance between it and 1 would be 0 simply because infinity isn't a measurable number. Therefore, yes 0.9r does equal 1. However, I also believe that my second concept is also true... this goes as follows. Based on the same theory, because there are infinite 9's in the 0.9r, it means that the distance between it and 1 is an infinitely imeasurable number. In other words, counting the number of decimal places you can go 0.9999...etc. all you want but you never actually get to the number 1. Given this, you can also say it's less than 1 therefore it isn't 1.
kingo	Date: September 16, 2005 @ 8:06 AM Pog: you certainly didn't tick me off, in case my comment about kicking you in the nuts is throwing you off. I do that to all my friends. I've had fun talking about this too, I've just been constantly frustrated. Your second option there is good for philosophical discussion but doesn't fit standard mathematics.
pog	Date: September 16, 2005 @ 8:30 AM Oh good... In that case, if you really do ever feel like kicking me in the nuts, then feel free to come down to and do so... there's always a to crash on and a fresh pot of on the stove I'm kinda fond of my second theory because the infinite 9's end up going round and round until they finally consume themselves in a black hole/vortex type of fashion mwaaahahahahaha
kingo	Date: September 16, 2005 @ 10:51 AM Well now you're talking. I've got no fashion sense, so I'll bow to your expertise on the matter of the .9... as related to same every time. And if I ever get the urge to run from the people running this asylum over here, I'll be keeping that in mind.
Intergalacti...	Date: September 16, 2005 @ 7:01 PM White men say, only fools rush in, but i can't stand falling in love with you
hantu	Date: September 17, 2005 @ 10:41 AM or maybe the train going there don't make it all the way but the train coming back does
Maffmatix	Date: September 17, 2005 @ 6:00 PM p=1 e=3 n=5 i=7 s=9 v=11 a=33 g=55 i=77 n=99 a=10 what do you get when you mix 25 with 285?!?! THAT'S MY KINDA MAFF
AdNauseam	Date: May 10, 2008 @ 5:45 PM infinity: (910^-i) The formula, of course, for the sum of the infinite geometric series ar^i is: [first term]/(1-r) The first term is .9, and r is .1 (10^-1, or 1/10) 1-.1 = .9 .9/.9 = 1
AdNauseam	Date: May 10, 2008 @ 5:50 PM that should read: .9... can be expressed as the infinite sum: sigma i=0 -- infinity: (910^-i) The formula, of course, for the sum of the infinite geometric series ar^i is: [first term]/(1-r) The first term is .9, and r is .1 (10^-1, or 1/10) 1-.1 = .9 .9/.9 = 1
Mojosnake	Date: May 10, 2008 @ 6:27 PM
Opossum	Date: May 10, 2008 @ 11:50 PM Isn't it funny how 2 x 2 = 4 ...and 2 PLUS 2 is ALSO 4? And isn't it weird that 12 x 12 = 144 when 24 (which is 12 x 2) x 6 (which is 12/2) is ALSO 144? The mind boggles.
killoFunk	Date: May 11, 2008 @ 2:33 AM Geeks always gotta screw things up.... if something is "countable"--- it's NOT INFINITE. Webster defined 'infinite' for a reason. UGH! It's no wonder this world is whack... and don't get me started on "uninstall"...
TameasDust	Date: May 11, 2008 @ 7:45 PM If you add one to infinity you still have infinity but if you subtract the same one that you added to infinity you no longer have infinity ... Any number that can be expressed is one smaller than infinity ... To write out infinity you will meet yourself seven times before you are finished
AdNauseam	Date: May 12, 2008 @ 12:56 PM or by calculus: 1-.9r = .0r1 = (infinitesimal), or 1/infinity this infintesimal can be expressed as dx for any arbitrary function f(x) integrated between 0 and 1 (the bounds of our calculation): int(1,0)(1*dx)= 1
AdNauseam	Date: May 12, 2008 @ 12:57 PM by the way, that's not a rigourous proof... just an outline
AdNauseam	Date: May 12, 2008 @ 1:03 PM On second thought, that was executing a logical fallacy.... ignore my second proof until I work it out by hand.
Opossum	Date: May 12, 2008 @ 8:29 PM You need a Cray computer.
NickSawyer	Date: May 13, 2008 @ 5:14 AM I find it funny how everyone is acting all smart and seplling crorretctl
Opossum	Date: May 14, 2008 @ 7:01 AM Okay, what about this? 2/3 = 0.6... But depending on where we stop, there will, of course, be variations and a marriage of Mister Seven to Mister Six or the Harem of Six. (They weren't even properly introduced - they just got to it.) Then we can get, using this example, using 1 2/3: 1.67 ^ 2 = 2.7889 1.667 ^ = 2.778889 1.6667 ^ 2 = 2.77788889 ... 1.666667 ^ 2 = 2.777778888889 etc. See the pattern? However, 1/3 is a different animal than 2/3 because .3... only has Mister Three, .33, .333, .3333, etc. So we could then say Mister Three is a bachelor and keeps to himself... Looking at .9... = 1 is really only due to distance relative to 9 in itself, as we might as well argue about .9898 or .9888, etc.
Opossum	Date: May 14, 2008 @ 7:03 AM Okay, that should read 1.667 ^ 2 = 2.778889 but you get the idea.
Opossum	Date: May 14, 2008 @ 7:07 AM You know, I think I made an error relating to order of palpitations, in use of expanded vacations.
AdNauseam	Date: May 14, 2008 @ 2:58 PM I sense a runcible lampoon...
Wildy1	Date: May 15, 2008 @ 6:33 AM
Rodrica	Date: May 15, 2008 @ 9:55 PM The only figures I understand are the ones that ppl want to pay into my bank account Nothing else matters

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