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(1 paradox)Why 0.999... is not equal to 1?

 Posts: 751 Add as FriendChallenge to a DebateSend a Message 2/28/2013 12:30:21 PMPosted: 5 years ago(1 paradox)Why 0.999... is not equal to 1?1/9 = 0.111...9 x 1/9 = 9 x 0.111...1 = 0.999...QEDI don't see the problem...
 Posts: 18,870 Add as FriendChallenge to a DebateSend a Message 2/28/2013 12:37:05 PMPosted: 5 years agoI love this:1. If you cut an apple into 9ths and measure it, each piece won't exactly be 1/9th.2. Ergo 0.999... =/= 13. Ergo AI4. Ergo God
 Posts: 14,501 Add as FriendChallenge to a DebateSend a Message 2/28/2013 12:44:34 PMPosted: 5 years ago"The current mathematic theory tells us, 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..."Check your premises.1 =/= 0.999... because 0.999... has a value that is not equal to 1.Q.E.D.It doesn't matter if it's infinitely long. You don't need to know the exact value of things to compare them. An ocean is larger than a swimming pool. Is that invalid because you can't measure the volume of the ocean? Of course not. Even if you could, you would not need to to determine the conclusion.#StandWithBossy
 Posts: 204 Add as FriendChallenge to a DebateSend a Message 2/28/2013 4:30:31 PMPosted: 5 years agoAt 2/28/2013 12:30:21 PM, Floid wrote:(1 paradox)Why 0.999... is not equal to 1?1/9 = 0.111...9 x 1/9 = 9 x 0.111...1 = 0.999...QEDI don't see the problem...You just blew my mind.
 Posts: 751 Add as FriendChallenge to a DebateSend a Message 3/1/2013 7:12:53 AMPosted: 5 years agoAt 2/28/2013 12:37:05 PM, drafterman wrote:I love this:1. If you cut an apple into 9ths and measure it, each piece won't exactly be 1/9th.Then you didn't really cut the apple into 9ths.
 Posts: 643 Add as FriendChallenge to a DebateSend a Message 3/1/2013 8:24:10 AMPosted: 5 years agoFor the apple part, it is about the degree of accuracy (just like the measurement of Pi). The modern technology can only go that far, therefore the measurement would not be absolutely perfect.
 Posts: 3,932 Add as FriendChallenge to a DebateSend a Message 3/1/2013 1:01:42 PMPosted: 5 years agoIf you took an object made of nine quarks, and removed one, there would be no theoretical inaccuracy in the size of the chunk you removed. However, until there is a technological solution as to achieving this, exactly, one can always say that such things are outside of our scope of influence.AKA Rob1billion Rob1_Billion Caramel Lasagna
 Posts: 14,501 Add as FriendChallenge to a DebateSend a Message 3/1/2013 1:07:54 PMPosted: 5 years agoAt 2/28/2013 12:30:21 PM, Floid wrote:(1 paradox)Why 0.999... is not equal to 1?1/9 = 0.111...9 x 1/9 = 9 x 0.111...1 = 0.999...QEDI don't see the problem...That doesn't make any theoretical sense.#StandWithBossy
 Posts: 751 Add as FriendChallenge to a DebateSend a Message 3/1/2013 9:31:59 PMPosted: 5 years agoThat doesn't make any theoretical sense.Please elaborate:Do you dispute that:1/9 = 0.111..9 x 1/9 = 19 x 0.111... = 0.999...or that for any real numbers a, b, and c, if a = b, then ac = bc
 Posts: 6,071 Add as FriendChallenge to a DebateSend a Message 3/2/2013 4:52:00 PMPosted: 5 years agoAt 2/28/2013 12:37:05 PM, drafterman wrote:I love this:1. If you cut an apple into 9ths and measure it, each piece won't exactly be 1/9th.2. Ergo 0.999... =/= 13. Ergo AI4. Ergo GodThe Fool: Wow you actually Proved God, Wow. I didn't think it could be done.I NOW SEE THE LIGHT!. @t the red light district."The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another." G. W. F. HEGEL
 Posts: 14,501 Add as FriendChallenge to a DebateSend a Message 3/2/2013 4:54:13 PMPosted: 5 years agoAt 3/1/2013 9:31:59 PM, Floid wrote:That doesn't make any theoretical sense.Please elaborate:Do you dispute that:1/9 = 0.111..9 x 1/9 = 19 x 0.111... = 0.999...or that for any real numbers a, b, and c, if a = b, then ac = bcBy definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.#StandWithBossy
 Posts: 63 Add as FriendChallenge to a DebateSend a Message 3/2/2013 8:15:11 PMPosted: 5 years agoCrikeys - it's like fighting over that extra penny when you split the check! Sort of makes your head want to explode, doesn't it?If your time, to you, Is worth savin', Then you better start swimmin' Or you'll sink like a stone. For the times they are a-changin'. - Bob Dylan
 Posts: 751 Add as FriendChallenge to a DebateSend a Message 3/2/2013 8:46:42 PMPosted: 5 years agoBy definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.Except I gave you a simple proof that demonstrates that they are equal and apparently you can't present an argument against any portion of that proof. Instead you just say "that can't be".Of course the formal reason that 0.999... = 1 would be stated:The limit as x -> infinity of (x-1)/x = 1But that really loses the fun of the simple algebraic example given above.
 Posts: 14,501 Add as FriendChallenge to a DebateSend a Message 3/2/2013 8:49:58 PMPosted: 5 years agoAt 3/2/2013 8:46:42 PM, Floid wrote:By definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.Except I gave you a simple proof that demonstrates that they are equal and apparently you can't present an argument against any portion of that proof. Instead you just say "that can't be".That's because contradictions cannot exist. One of your premises have to be wrong.Of course the formal reason that 0.999... = 1 would be stated:The limit as x -> infinity of (x-1)/x = 1But that really loses the fun of the simple algebraic example given above.So are you saying that .999 repeating is not .999 repeating?#StandWithBossy
 Posts: 751 Add as FriendChallenge to a DebateSend a Message 3/2/2013 9:28:18 PMPosted: 5 years agoThat's because contradictions cannot exist. One of your premises have to be wrong.So point it out, which one is wrong?So are you saying that .999 repeating is not .999 repeating?I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?But if it must be spelled out for you:0.999... is equal to 0.999...0.999... is equal to 1Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.
 Posts: 14,501 Add as FriendChallenge to a DebateSend a Message 3/2/2013 9:36:29 PMPosted: 5 years agoAt 3/2/2013 9:28:18 PM, Floid wrote:That's because contradictions cannot exist. One of your premises have to be wrong.So point it out, which one is wrong?.999 repeating equaling 1.So are you saying that .999 repeating is not .999 repeating?I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?I would if A is by definition not B.But if it must be spelled out for you:0.999... is equal to 0.999...0.999... is equal to 1Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.If 0.999... is 0.999..., then it is not 1. That would be like saying that 1 = 2. 1 does not equal 2 because 1 by definition has a different value than 2.#StandWithBossy
 Posts: 1,023 Add as FriendChallenge to a DebateSend a Message 3/2/2013 10:24:29 PMPosted: 5 years agoAt 3/2/2013 9:36:29 PM, bossyburrito wrote:At 3/2/2013 9:28:18 PM, Floid wrote:That's because contradictions cannot exist. One of your premises have to be wrong.So point it out, which one is wrong?.999 repeating equaling 1.So are you saying that .999 repeating is not .999 repeating?I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?I would if A is by definition not B.But if it must be spelled out for you:0.999... is equal to 0.999...0.999... is equal to 1Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.If 0.999... is 0.999..., then it is not 1. That would be like saying that 1 = 2. 1 does not equal 2 because 1 by definition has a different value than 2.Clearly if 3/3 is 3/3, then it is not 1.
 Posts: 14,501 Add as FriendChallenge to a DebateSend a Message 3/2/2013 11:16:08 PMPosted: 5 years agoAt 3/2/2013 10:24:29 PM, Enji wrote:At 3/2/2013 9:36:29 PM, bossyburrito wrote:At 3/2/2013 9:28:18 PM, Floid wrote:That's because contradictions cannot exist. One of your premises have to be wrong.So point it out, which one is wrong?.999 repeating equaling 1.So are you saying that .999 repeating is not .999 repeating?I would say their is no point in stating a tautology. If I were to say A = B you wouldn't turn around and ask me "Are you saying A is not equal to A?" now would you?I would if A is by definition not B.But if it must be spelled out for you:0.999... is equal to 0.999...0.999... is equal to 1Both of the above statements are mathematically true and demonstrated through the simple algebraic proof I included above and embodied in the idea of limits, a key concept used in many areas of mathematics.If 0.999... is 0.999..., then it is not 1. That would be like saying that 1 = 2. 1 does not equal 2 because 1 by definition has a different value than 2.Clearly if 3/3 is 3/3, then it is not 1.By definition it is one. 0.999... is not equal to 1 because it is 0.999... and not one.#StandWithBossy
 Posts: 25,980 Add as FriendChallenge to a DebateSend a Message 3/3/2013 2:25:40 AMPosted: 5 years agoAt 3/2/2013 4:54:13 PM, bossyburrito wrote:At 3/1/2013 9:31:59 PM, Floid wrote:That doesn't make any theoretical sense.Please elaborate:Do you dispute that:1/9 = 0.111..9 x 1/9 = 19 x 0.111... = 0.999...or that for any real numbers a, b, and c, if a = b, then ac = bcBy definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.No, it does, that is the thing. You are saying "by definition" but that is not true."Wanting Red Rhino Pill to have gender"
 Posts: 25,980 Add as FriendChallenge to a DebateSend a Message 3/3/2013 2:28:30 AMPosted: 5 years agoThe OP would also be suggesting that all limits are thus false, though we can test and prove them to be true through application. Most notably the Taylor series for SIN and COS."Wanting Red Rhino Pill to have gender"
 Posts: 3,667 Add as FriendChallenge to a DebateSend a Message 3/3/2013 5:06:53 AMPosted: 5 years agoHere's the most ridiculous result in mathematics I've come across:1=(2-1)(1+2+4+8...) - - >infinite series where each number is double the last.=1*(1+2+4+8...)=(2-1)(1+2+4+8...)Multiply out the brackets.2+4+8+16...-1-2-4-8...Every number except -1 cancels out --> -1 = (1+2+4+8...)
 Posts: 14,501 Add as FriendChallenge to a DebateSend a Message 3/3/2013 5:23:33 AMPosted: 5 years agoAt 3/3/2013 2:25:40 AM, Ore_Ele wrote:At 3/2/2013 4:54:13 PM, bossyburrito wrote:At 3/1/2013 9:31:59 PM, Floid wrote:That doesn't make any theoretical sense.Please elaborate:Do you dispute that:1/9 = 0.111..9 x 1/9 = 19 x 0.111... = 0.999...or that for any real numbers a, b, and c, if a = b, then ac = bcBy definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.No, it does, that is the thing. You are saying "by definition" but that is not true.If 0.999 repeating is equal to one, doesn't that mean that it is 0.999 repeating to infinity until a 1 at the end? You can't have an end to infinity.#StandWithBossy
 Posts: 63 Add as FriendChallenge to a DebateSend a Message 3/3/2013 6:04:49 AMPosted: 5 years agoAt 3/2/2013 8:15:11 PM, Cinco wrote:Crikeys - it's like fighting over that extra penny when you split the check! Sort of makes your head want to explode, doesn't it?Totally forgot - it's just a clash of perspectives. I have stepped across the threshold! Hallelujah! I LOVE a brain tilt!! Thanks!If your time, to you, Is worth savin', Then you better start swimmin' Or you'll sink like a stone. For the times they are a-changin'. - Bob Dylan
 Posts: 1,023 Add as FriendChallenge to a DebateSend a Message 3/3/2013 10:56:45 AMPosted: 5 years agoAt 3/3/2013 5:23:33 AM, bossyburrito wrote:At 3/3/2013 2:25:40 AM, Ore_Ele wrote:At 3/2/2013 4:54:13 PM, bossyburrito wrote:At 3/1/2013 9:31:59 PM, Floid wrote:That doesn't make any theoretical sense.Please elaborate:Do you dispute that:1/9 = 0.111..9 x 1/9 = 19 x 0.111... = 0.999...or that for any real numbers a, b, and c, if a = b, then ac = bcBy definition 0.999... does not equal 1. If it did then it would be 1. That is like saying that if a has a different value than b, a=b.No, it does, that is the thing. You are saying "by definition" but that is not true.If 0.999 repeating is equal to one, doesn't that mean that it is 0.999 repeating to infinity until a 1 at the end? You can't have an end to infinity.It means that .9999 repeating infinitely has the same value as 1, as is shown with various mathematical proofs of differing rigor.
 Posts: 9,578 Add as FriendChallenge to a DebateSend a Message 3/3/2013 12:55:26 PMPosted: 5 years agoI think that this is more of a limitation of a decimal numerical system than any sort of profound statement."Partout ou vous verrez un autel, la se trouve la civilisation." - Joseph de Maistre - "Woe that I live in bitter days, As God is setting like a sun And in his place, as lord and slave, Man raises forth his heinous throne." - Translation of 'Rhyfel', by Hedd Wyn - Virtutem videant intabescantque relicta
 Posts: 25,980 Add as FriendChallenge to a DebateSend a Message 3/3/2013 9:20:29 PMPosted: 5 years agoAt 3/3/2013 5:06:53 AM, Kinesis wrote:Here's the most ridiculous result in mathematics I've come across:1=(2-1)(1+2+4+8...) - - >infinite series where each number is double the last.=1*(1+2+4+8...)=(2-1)(1+2+4+8...)Multiply out the brackets.2+4+8+16...-1-2-4-8...Every number except -1 cancels out --> -1 = (1+2+4+8...)The limit of (1+2+4+8+16...2^n...) as n -> infinite does not exist, so it cannot be used in a proof."Wanting Red Rhino Pill to have gender"
 Posts: 6,924 Add as FriendChallenge to a DebateSend a Message 3/4/2013 12:12:37 AMPosted: 5 years agoAt 3/3/2013 12:55:26 PM, Skepsikyma wrote:I think that this is more of a limitation of a decimal numerical system than any sort of profound statement.Bingo.
 Posts: 3,667 Add as FriendChallenge to a DebateSend a Message 3/4/2013 4:24:38 AMPosted: 5 years agoAt 3/3/2013 9:20:29 PM, Ore_Ele wrote:At 3/3/2013 5:06:53 AM, Kinesis wrote:Here's the most ridiculous result in mathematics I've come across:1=(2-1)(1+2+4+8...) - - >infinite series where each number is double the last.=1*(1+2+4+8...)=(2-1)(1+2+4+8...)Multiply out the brackets.2+4+8+16...-1-2-4-8...Every number except -1 cancels out --> -1 = (1+2+4+8...)The limit of (1+2+4+8+16...2^n...) as n -> infinite does not exist, so it cannot be used in a proof.I wasn't aware that was a rule. Point to something explaining why that is? (or explain it).
 Posts: 1,321 Add as FriendChallenge to a DebateSend a Message 3/4/2013 4:42:28 AMPosted: 5 years agoAt 2/28/2013 12:30:21 PM, Floid wrote:(1 paradox)Why 0.999... is not equal to 1?1/9 = 0.111...9 x 1/9 = 9 x 0.111...1 = 0.999...QEDI don't see the problem...1>0.999... by a total of 0.000... for math to actually work. Otherwise every number in existence is rounded once the number exceeds 0.999... I think"So you want me to go to the judge with 'unit, corps, God, country'?" - A Few Good Men "And the hits just keep on comin'." -A Few Good Men