1=.999...

Pre-College Issues High School Life
21

<p>To Generally Wrong:
That proof is wrong because there is division by zero, which is not allowed in proofing. And on the concept of .999. If I were in AP Chem it would depend on what values are used to determine it. Significant figures may cause the value to be rounded up, thus making it 1. (as far as measurement goes)</p>

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<p>.99999… exactly equals 1 without rounding, significant digits, or otherwise changing the value.</p>

<p>1/3=0.333…</p>

<p>0.333… x 3=0.999…</p>

<p>1/3 x 3=3/3=1 Or 0.333… x 3=1</p>

<p>Ergo: 0.999… exactly equals 1 or 1-0.999…=0</p>

<p>Some people will never understand it. <em>palmface</em></p>

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<p>For those of you who say they’re not equal, what is 1 minus .999…?</p>

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<p>I’m a believer!</p>

<p>There’s a thread in the MIT forum and one in the cafe with more information (see the suggested list of topics below).</p>

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<p>It is irrelevant whether .999… equals 1 or not.</p>

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<p>^^^^^also because in writing out x^2 as x…x you assume x is a natural number, and you can’t take the derivative of a function that’s only defined on the natural numbers.</p>

<p>(f must be defined on an open subset of R)</p>

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<p>1 ≥ .999 ?</p>

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<p>Once you get past about 10^-20 m you get to the atomic scale, which we don’t know that much about and can’t measure directly, therefore you really have no business arguing about this. Unless you’re a mathematician.</p>

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<p>0.[repeating digits] = [repeating digits]/[the same number of digits, except all are 9]
0.[repeating 9] = 9/9 = 1</p>

<p>0.999… = -e^(i*pi)</p>

<p>discuss.</p>

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<p>I’m sure Euler didn’t spend this long on a numerical problem.</p>

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<p>I agree with 0.999… = 1</p>

<p>Simply put:
1/3 = 0.333…
2/3 = 0.666…
3/3 = 0.999… = 1</p>

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<p>Let S = 1-1/2+1/3-1/4+1/5-1/6+1/7-1/8+…</p>

<p>Notice, 1-1/2 = 1/2, 1/3-1/6 = 1/6, 1/5-1/10 = 1/10, etc.</p>

<p>and we also have -1/4, -1/8, -1/12, etc.</p>

<p>Thus, S = 1/2-1/4+1/6-1/8+…</p>

<p>Or S = 2S, thus 1 = 2.</p>

<p>Discuss. (Btw, S converges to ln 2).</p>

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<p>More precisely: [Planck</a> length - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Planck_length]Planck”>Planck units - Wikipedia)</p>

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<p>^^mindblowing ain’t it
[Riemann</a> Series Theorem – from Wolfram MathWorld](<a href=“http://mathworld.wolfram.com/RiemannSeriesTheorem.html]Riemann”>Riemann Series Theorem -- from Wolfram MathWorld)</p>

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<p>A Wharton mathematician is not like a Caltech mathematician… HAHAAHA… KNOW WHAT I MEAN!!! Try telling a business man that 0.0999… Is equal to 1. now seriously… IT’S ALL ABOUT TRANSETIVE PROPERTIES!</p>

<p>1/3=0.33333333333…
=>1/3<em>2=0.66666666…
=>0.6666666</em>1.5 which is ultimately 1/3*2 is EQUAL TO 1!</p>

<p>Over… Depends on what kinda person you are. Wharton Vs. Caltech right here. lol.</p>

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<p>Yeah, apparently Wharton math =/= Caltech math.</p>

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<p>Interesting logic Lobzz. I was not aware that (1/3<em>2) * 1.5 = 1/3</em>2.</p>

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<p>It is irrelevant whether you recognize the relevance of the equality or not.</p>

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<p>The ability or inability of one to measure a difference or the relevancy of said difference is not relevant to whether 1 and .9… are in fact the same number NOT whether or not there is any reasonable difference between them.</p>

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<p>I disagree because I’m stubborn like that</p>

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<p>This idea frustrated me as a young child.</p>

<p>I sought help and I now accept it, though. My mathematical therapist, who was very expensive, said to think of the 9’s as placards on happy marker boards. When the bubbly frog of happiness and joy, who was flipping the placards, gets to the end of the series of many, many happy marker boards, the 9’s start on a domino effect until they get to the first 9 and change it to a 0 and push a one before the decimal point of equal happiness.</p>