Altαir Posted September 6, 2009 Report Share Posted September 6, 2009 No' date=' 0.999999... =/ 1 Many numbers have the same problem. 1/3 = 0.3333... BUT 0.33333... x 3 =/ 1. YET 0.999.../3 = 0.333... AND 0.333... x 3 = 0.999...[/quote'] 1/3 = 0.333...Therefore:0.333... x 3 = 0.999... (using your logic) X/X = 1Therefore:3/3 = 1 (using simple math) 1 = 3/33/3 = 3 x 1/33 x 1/3 = 3 x 0.333...3 x 0.333... = 0.999... Therefore: 1 = 0.999... If that is not true, what did I do wrong? EDIT: Also: 1/3 = 0.333...Therefore:1 / 3 = 0.333... 0.999... / 3 = 0.333... 0.999... / 3 = 1 / 3 Multiply by 3. 0.999... = 1 But you proved that 3 x 0.333... = 0.999... in the first one. The second one, you beat me. But, 1 cannot equal 0.999... Before I go on to my next topic, have you learned of imaginary numbers in school? Link to comment Share on other sites More sharing options...
Dark Posted September 6, 2009 Author Report Share Posted September 6, 2009 Right, but 3 x 0.333... (which is 1/3) also equals 1. And yes, I have learned about imaginary numbers. I am in 11th grade. :/ Link to comment Share on other sites More sharing options...
Altαir Posted September 6, 2009 Report Share Posted September 6, 2009 Oh. Then could 0.333...4 be an imaginaary number? If not, then I have Lost the Game... Link to comment Share on other sites More sharing options...
Pikachu Posted September 6, 2009 Report Share Posted September 6, 2009 That is exactly why they invented fractions. Link to comment Share on other sites More sharing options...
Lord.Alucard. Posted September 6, 2009 Report Share Posted September 6, 2009 I tried reading this and I my head started hurting. Link to comment Share on other sites More sharing options...
Kizzi Posted September 6, 2009 Report Share Posted September 6, 2009 It couldn't possibly be 0.333...4, because there's no end to stick the four on. This also means that 0.000...1 must = 0. Link to comment Share on other sites More sharing options...
Dark Posted September 6, 2009 Author Report Share Posted September 6, 2009 Oh. Then could 0.333...4 be an imaginaary number? If not' date=' then I have Lost the Game...[/quote'] That's the same problem with 0.000...1, the one would never actually have a value because of the infinite zero's preceding it. And if 0.333...4 was a number, it would either be 1/3 (due to the problem listed above) or irrational. It couldn't possibly be 0.333...4' date=' because there's no end to stick the four on. This also means that 0.000...1 must = 0.[/quote'] Does that prove that 0.999... equals 1, or is that still unsolved? Link to comment Share on other sites More sharing options...
Huntar! Posted September 6, 2009 Report Share Posted September 6, 2009 I am assuming that 0.999... equals 1 based on the fact that 3 x 0.333... also equals one. Well, .333..... repeating infinitely with 3's will never equal 1 when multiplied by 3. Eventually to equal 1 it will have to end in a 4 when added with 2 infinitely repeating .333's. No matter how close it gets. And still, any number that even has a very small digit above 0 is not 0 itself. 0 is meant to be nothing. And .0000000000.........1 is still above 0. Link to comment Share on other sites More sharing options...
Dark Posted September 6, 2009 Author Report Share Posted September 6, 2009 There is a flaw in your logic. 1/3 = 0.333... 1/3 x 3 = 3/3 = 10.333... x 3 = 0.999... That means 1 = 0.999... Link to comment Share on other sites More sharing options...
Huntar! Posted September 6, 2009 Report Share Posted September 6, 2009 There is a flaw in your logic. 1/3 = 0.333... 1/3 x 3 = 3/3 = 10.333... x 3 = 0.999... That means 1 = 0.999... 1/3 = .33333..., yes. And 3/3 makes 1, yes. But .333... x 3 does not equal 1. It equals a never ending decimal, which never equals 1 no matter how hard it tries. It works one way, but not the other. Link to comment Share on other sites More sharing options...
Kizzi Posted September 6, 2009 Report Share Posted September 6, 2009 I am assuming that 0.999... equals 1 based on the fact that 3 x 0.333... also equals one. Well' date=' .333..... repeating infinitely with 3's will never equal 1 when multiplied by 3. Eventually to equal 1 it will have to end in a 4 when added with 2 infinitely repeating .333's. No matter how close it gets. And still, any number that even has a very small digit above 0 is not 0 itself. 0 is meant to be nothing. And .0000000000.........1 is still above 0.[/quote'] Incorrect - it's impossible. Unless you're using the ellipses to represent something other than infinity repetition of the number before it? There is a flaw in your logic. 1/3 = 0.333... 1/3 x 3 = 3/3 = 10.333... x 3 = 0.999... That means 1 = 0.999... 1/3 = .33333...' date=' yes. And 3/3 makes 1, yes. But .333... x 3 does not equal 1. It equals a never ending decimal, [b']which never equals 1 no matter how hard it tries[/b]. It works one way, but not the other. Proof? Link to comment Share on other sites More sharing options...
Dark Posted September 6, 2009 Author Report Share Posted September 6, 2009 There is a flaw in your logic. 1/3 = 0.333... 1/3 x 3 = 3/3 = 10.333... x 3 = 0.999... That means 1 = 0.999... 1/3 = .33333...' date=' yes. And 3/3 makes 1, yes. But .333... x 3 does not equal 1. It equals a never ending decimal, which never equals 1 no matter how hard it tries. It works one way, but not the other.[/quote'] *facepalm* No, you are not an idiot. I just don't think you are grasping what I am saying. 1/3 = 0.333... Since they are equal values, they can be interchanged. Like 2 and 2/1. 1/3 x 3 = 3/3 Basic multiplication. 3/3 = 1 Basic division. That's part one. 0.333... x 3 = 0.999... That is simple infinite multiplication. That's part two. And now, let's put it together. 1/3 x 3 = 10.333... x 3 = 0.999... And we stated earlier that 1/3 and 0.333... can be interchanged as they are equal. 0.333... x 3 = 1 Likewise... 1/3 x 3 = 0.999... Link to comment Share on other sites More sharing options...
Recommended Posts
Archived
This topic is now archived and is closed to further replies.