Spec138 Posted April 3, 2009 Share Posted April 3, 2009 question: the area of the function y<x is equal to the area of the function of y<=x. Does that mean that y<x == y<=x? Area of a function? edit: Are you talking integral? Link to comment Share on other sites More sharing options...
Coach Williams Posted April 3, 2009 Share Posted April 3, 2009 is there really 8 pages discussing this? The answer is CLEARLY a "maybe" Link to comment Share on other sites More sharing options...
Spec138 Posted April 3, 2009 Share Posted April 3, 2009 is there really 8 pages discussing this? The answer is clearly a "yes" fify Link to comment Share on other sites More sharing options...
Slacky McSlackAss Posted April 3, 2009 Share Posted April 3, 2009 .999 repeating is a decimal value, which is not an integer. 1 is an integer so they are clearly not the same. Link to comment Share on other sites More sharing options...
Spec138 Posted April 4, 2009 Share Posted April 4, 2009 .999 repeating is a decimal value, which is not an integer. 1 is an integer so they are clearly not the same. Tell me, what is the number between .999... and 1? Link to comment Share on other sites More sharing options...
Mark The Homer Posted April 4, 2009 Share Posted April 4, 2009 In theory, the answer is no. Because there will always be a gap. In practical application, the answer is yes. Because the gap is infinitely small. Link to comment Share on other sites More sharing options...
SkinsKin26 Posted April 4, 2009 Share Posted April 4, 2009 I say they are equal. There's a funner geometric series proof, but I don't have time to post it now, so I'll update later. Here's one though I really like. x = .9 repeating 10x = 9.9 repeating 10x -x = 9.9 repeating - .9 repeating 9x = 9 x = 1 so 1 = .9 repeating Link to comment Share on other sites More sharing options...
Spec138 Posted April 4, 2009 Share Posted April 4, 2009 In theory, the answer is no. Because there will always be a gap.In practical application, the answer is yes. Because the gap is infinitely small. In theory the answer is actually yes. .999... is not a decimal, it's simply another way of expressing 1. I could show another proof as well. Link to comment Share on other sites More sharing options...
Larry Posted April 4, 2009 Share Posted April 4, 2009 is there really 8 pages discussing this? The answer is CLEARLY a "maybe" I figured my post would at least be good for a hijack: The real question is does 36C, repeating = 36D? Or is 36CC different then 36D?Useless without pics. Link to comment Share on other sites More sharing options...
Mark The Homer Posted April 4, 2009 Share Posted April 4, 2009 I say they are equal. There's a funner geometric series proof, but I don't have time to post it now, so I'll update later. Here's one though I really like.x = .9 repeating 10x = 9.9 repeating 10x -x = 9.9 repeating - .9 repeating 9x = 9 x = 1 so 1 = .9 repeating Damn. That's pretty good. I don't see any fault in it. Link to comment Share on other sites More sharing options...
Mark The Homer Posted April 4, 2009 Share Posted April 4, 2009 In theory the answer is actually yes..999... is not a decimal, it's simply another way of expressing 1. I could show another proof as well. I stand corrected. Link to comment Share on other sites More sharing options...
ACW Posted April 4, 2009 Share Posted April 4, 2009 Technically, NO. .9999999999999999999999999999999999999999999999999 does not equal 1 Link to comment Share on other sites More sharing options...
PokerPacker Posted April 4, 2009 Share Posted April 4, 2009 Tell me, what is the number between .999... and 1? we. live. in. a. continuous. world. Discrete. measures. are. not. an. accurate. portrayal. of. reality. Link to comment Share on other sites More sharing options...
Mark The Homer Posted April 4, 2009 Share Posted April 4, 2009 Technically, NO..9999999999999999999999999999999999999999999999999 does not equal 1 Dude, look at the proof above. Find a fault in it. Link to comment Share on other sites More sharing options...
ACW Posted April 4, 2009 Share Posted April 4, 2009 Dude, look at the proof above. Find a fault in it.Just found it:.9*10=9.0 Link to comment Share on other sites More sharing options...
Spec138 Posted April 4, 2009 Share Posted April 4, 2009 we. live. in. a. continuous. world.Discrete. measures. are. not. an. accurate. portrayal. of. reality. Doesn't change the fact that .999... = 1. I've seen some arguements that even if you go to a billion 9's in .99999999 (to a billion 9's) that it is not equal to 1. The entire flaw of this is that 1 billion =/= infinity. Btw this wasn't to you poker. Link to comment Share on other sites More sharing options...
Mark The Homer Posted April 4, 2009 Share Posted April 4, 2009 Just found it:.9*10=9.0 There is no .9 in the proof. It's a repeating .9 Link to comment Share on other sites More sharing options...
Slacky McSlackAss Posted April 4, 2009 Share Posted April 4, 2009 lets say you start off at point 0. and every step you take you get half way closer to point 1. YOU WILL NEVER REACH POINT ONE!!!! EVER. But the difference between the two will be so infinitesimal that we just say that you arrive at point one. Here is what you would get if you were to run a program that would calculate this. x=0.0 x=0.5 x=0.75 x=0.875 x=0.9375 x=0.96875 x=0.984375 x=0.9921875 x=0.99609375 x=0.998046875 x=0.9990234375 x=0.99951171875 x=0.999755859375 x=0.9998779296875 x=0.99993896484375 x=0.999969482421875 x=0.9999847412109375 x=0.9999923706054688 x=0.9999961853027344 x=0.9999980926513672 x=0.9999990463256836 x=0.9999995231628418 x=0.9999997615814209 x=0.9999998807907104 x=0.9999999403953552 x=0.9999999701976776 x=0.9999999850988388 x=0.9999999925494194 x=0.9999999962747097 x=0.9999999981373549 x=0.9999999990686774 x=0.9999999995343387 x=0.9999999997671694 x=0.9999999998835847 x=0.9999999999417923 x=0.9999999999708962 x=0.9999999999854481 x=0.999999999992724 x=0.999999999996362 x=0.999999999998181 x=0.9999999999990905 x=0.9999999999995453 x=0.9999999999997726 x=0.9999999999998863 x=0.9999999999999432 x=0.9999999999999716 x=0.9999999999999858 x=0.9999999999999929 x=0.9999999999999964 x=0.9999999999999982 x=0.9999999999999991 x=0.9999999999999996 x=0.9999999999999998 x=0.9999999999999999 Link to comment Share on other sites More sharing options...
Larry Posted April 4, 2009 Share Posted April 4, 2009 we. live. in. a. continuous. world.Discrete. measures. are. not. an. accurate. portrayal. of. reality. If. there. is. no. number. between. them. comma. then. they. are. the. same. number. period. Link to comment Share on other sites More sharing options...
Mark The Homer Posted April 4, 2009 Share Posted April 4, 2009 I say they are equal. There's a funner geometric series proof, but I don't have time to post it now, so I'll update later. Here's one though I really like.x = .9 repeating 10x = 9.9 repeating 10x -x = 9.9 repeating - .9 repeating 9x = 9 x = 1 so 1 = .9 repeating You guys need to look at this. If you can't find a fault in this, then you have to accept it. I've accepted it. Edit: Slacky, your computer only goes to 16 places. It would have to go to an infinite number of places to be of any use in this situation. Therefore, it's useless. Link to comment Share on other sites More sharing options...
Slacky McSlackAss Posted April 4, 2009 Share Posted April 4, 2009 This is worse than the political threads. :doh: Link to comment Share on other sites More sharing options...
Larry Posted April 4, 2009 Share Posted April 4, 2009 lets say you start off at point 0. and every step you take you get half way closer to point 1. YOU WILL NEVER REACH POINT ONE!!!! EVER. But the difference between the two will be so infinitesimal that we just say that you arrive at point one. Which has nothing to do with the question. The proof presented is a valid mathematical proof. It is 100%, absolutely, without question, proven. All of these "well, no matter how many 9's you have" thought exercises are nothing more than changing the question. Because no matter how many 9's you have, it won't be an infinite number of 9's. And the problem specified an infinite number. Link to comment Share on other sites More sharing options...
Larry Posted April 4, 2009 Share Posted April 4, 2009 This is worse than the political threads. :doh: Not quite. 1) It's conceivable that some people in this thread will change their position. Some may even admit that they were wrong. 2) And it's highly unlikely that there will be another thread, a month from now, in which exactly the same people will post exactly the same "reasoning". Link to comment Share on other sites More sharing options...
Slacky McSlackAss Posted April 4, 2009 Share Posted April 4, 2009 You guys need to look at this. If you can't find a fault in this, then you have to accept it. I've accepted it. Slacky, your computer only goes to 16 places. Therefore, it's useless. Find me a computer that goes to 200 or 300 and you will see the same thing. It will never be exactly 1, but will continue to repeat 9s. Link to comment Share on other sites More sharing options...
Mark The Homer Posted April 4, 2009 Share Posted April 4, 2009 Find me a computer that goes to 200 or 300 and you will see the same thing. It will never be exactly 1, but will continue to repeat 9s.300 places is infinitely short of what you need.Look at the proof. You can't refuse to accept the truth when it's staring you in the face. Link to comment Share on other sites More sharing options...
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