[ARCHIVED THREAD] - 1.99... = 2 (Page 1 of 13)
Posted: 6/3/2015 9:37:40 PM EDT
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1.999 repeating = 2.
Edit: poll should read 1.99999... |
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Yes, 1.99999… (repeating to infinity) is equal to 2.
It certainly is a practical matter. Imagine one apple plus .999999… of an apple. That’s two apples. I would say that you aren’t going to worry about that missing electron in the apple, but that’s overstating things. You aren’t even missing one atom, one electron, one quark, from the second apple. There wouldn’t be one bit of difference. And in pure math, if you wind up with .99999… you probably divided by 3 somewhere and then the difference is just caused by an artifact of the way we write numbers… One third is 0.333333… Three times one third is obviously one but it is also 0.999999… |
If you are my wife and something costs $1.99 then you will come home and tell me you bought it because "It was only $1." Of course, that scenario usually happens with numbers that are 100x that amount - e.g. Worthless widget costs $199 and my wife comes home and says, "I had to buy it because it was only $100."
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Originally Posted By happycynic: It is the 1 that throws everything off. Just do the .99 bar by itself. 1 / 3 = 1/3 1 / 3 = .33bar 1/3 x 3 = 3/3 .33bar x 3 = .99bar 3/3 = .99bar = 1 Then 1 + 1 = 2 1 + .99bar = 1.99bar 1.99bar = 2 Originally Posted By happycynic: Originally Posted By scul: I still say no, despite being able to force the math. 1 / 3 = 1/3 1 / 3 = .33bar 1/3 x 3 = 3/3 .33bar x 3 = .99bar 3/3 = .99bar = 1 Then 1 + 1 = 2 1 + .99bar = 1.99bar 1.99bar = 2 then 1/3 =/= .33bar It is in fact an artifact of decimal notation. .99bar = 1 1/3 can not be represented correctly in base 10. |
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There's an infinite amount of numbers between 1.9999 and 2. Literally. Quoted:
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they're equal if not, then show me the number between 1.9999... and 2 There's an infinite amount of numbers between 1.9999 and 2. Literally. True, but there are no numbers between 1.9repeating and 1. Therefore they are equal. 1.9repeating is not even infinitely close to 1 but not 1. It's just like i said above, find the solution for Zeno's paradox and apply it to this problem. If you can walk across a room then 1.9repeating equals 2. |
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As a full-time algebra teacher in a private school not represented by a union and getting paid by the hour and who does not get a summer vacation because I'm not getting paid if I don't work who is certified by the Great State of Texas to teach a multitude of subjects including Algebra, the answer is no.
1.99999999999999999 ad infinitum does not equal 2. I am also certified to teach economics and many other social studies. And as such, we can assume 1.999999999999999 ad infinitum equals 2 because economists make shit up all the time. Did you know if you were to lay all economists end to end they still wouldn't reach a conclusion? |
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if 1/3 x 3 = 1 and .33bar x 3 = .99bar then 1/3 =/= .33bar It is in fact an artifact of decimal notation. .99bar = 1 1/3 can not be represented correctly in base 10. Quoted:
Originally Posted By happycynic:
Originally Posted By scul:
I still say no, despite being able to force the math. 1 / 3 = 1/3 1 / 3 = .33bar 1/3 x 3 = 3/3 .33bar x 3 = .99bar 3/3 = .99bar = 1 Then 1 + 1 = 2 1 + .99bar = 1.99bar 1.99bar = 2 then 1/3 =/= .33bar It is in fact an artifact of decimal notation. .99bar = 1 1/3 can not be represented correctly in base 10. 
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Quoted:
There's an infinite amount of numbers between 1.9999 and 2. Literally. Quoted:
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they're equal if not, then show me the number between 1.9999... and 2 There's an infinite amount of numbers between 1.9999 and 2. Literally. Something occurred to me just now. In quantum physics there are the concepts of Planck length and planck time. Basically these represent the smallest amount of time or length you can have that can theoretically be measured. at distances less than Planck length, two points cannot be distinguished from each other. since numbers are typically used to measure things, perhaps the addition of more 9s in .99bar becomes meaningless when reach Planck type values for whatever we are measuring. At that point if the universe rounds up, then .99bar does equal 1. If it doesn't round up, then .99bar does not equal 1. Just a thought I had. It assumes Planck length and time have some sort of significance in physics, something that is not known for certain. |
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No context needed. Either 1.99999999999... equals 2 or it doesn't. Quoted:
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Context. No context needed. Either 1.99999999999... equals 2 or it doesn't. The only time context isn't needed is when the objective of the person asking the question isn't to find the correct answer, but to start an argument. |
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As a full-time algebra teacher in a private school not represented by a union and getting paid by the hour and who does not get a summer vacation because I'm not getting paid if I don't work who is certified by the Great State of Texas to teach a multitude of subjects including Algebra, the answer is no. 1.99999999999999999 ad infinitum does not equal 2. I am also certified to teach economics and many other social studies. And as such, we can assume 1.999999999999999 ad infinitum equals 2 because economists make shit up all the time. Did you know if you were to lay all economists end to end they still wouldn't reach a conclusion? Show your work or your answer is incorrect. And none of that you cannot subtract 5 from 4 hippie shit. Either we are following the accepted rules of mathematics or we are not. f you want to get real then there is no such thing as 1.9 so on to bite em to infinitum. Sorry, to much rum makes me a belligerent mathematician. |