<p>1/infinity is not “proper” math. What you really mean is limit as n approaches infinity of 1/n. That does equal 0.</p>
<p>Anyways, think of this. If two numbers are different, then there is a number that comes between them right? So what number comes between 0.99999… and 1?</p>
<p>Easy. 0.000…1</p>
<p>lol.</p>
<p>x = 0.9999999… (… for infinitely repeating)
10x = 9.999999…
10x - x = 9.999… - .9999999…
9x = 9</p>
<p>x = 1.</p>
<p>Close, soggy_daisy, but…</p>
<p>x = 0.999…
10x = 9.999…0
10x - x = 9.999…0 - 0.999…
9x = 8.999…81
x = 0.999…</p>
<p>By the way, the notation x.xxx…x means “an infinite number of whatevers, ending with a whatever.” I know that totally blew your mind.</p>
<p>writing “lol” at the end of your “proof” doesn’t have quite the same force as writing “QED”, and in fact, seems to make me take your argument less seriously. But anyways, mine’s not a formal proof either. Soggy_Daisy and noimagination have proven it well enough.</p>
<p>@Auburn: there is no zero at the end of the 10x value. How can there be? With 9s continuing on to infinity, what can you multiply by that to get a zero at the end? For that matter, there is no “end” to the infinitely repeating decimal at all. That’s the whole point of an infinitely repeating decimal.</p>
<p>@auburn; hawkings is right.</p>
<p>btw, are you just joking or are you being serious here?</p>
<p>Jeez, you guys need to pay more attention. I’m obviously joking. Read my first post.</p>
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<p>Yeah, I got sloppy ;)</p>
<p>1/3 = .3333333…
2/3 = .6666666…
3/3 = ???..</p>
<p>3/3 = 1 =/= 0.999…</p>
<p>hmmm . . . interesting . . .</p>
<p>does a number by any other name become as hard 2 calculate !?!?</p>
<p>it’s good 2 know that there are some major controversies over in the math dept. . . .</p>
<p>auburn math tutor, did you take calc 2? 9.999… can be represented as 9/1+9/10+9/100+… or more concisely as sigma(9/(10^n),0,inf) is a geometric series, the formula for the convergence of which is a/(1-r) where a=9 and r=1/10, so 9/(1-1/10)=9/(9/10)=10. therefore 10=9.999… if you want exactly the OP subtract off 9 from each side, but you get the idea, everyone learns how to do this equation freshman year, though most don’t realize it.</p>
<p>silence kit, this is not a controversy, this is something that was proved ages ago. just because some people don’t understand the math behind it doesn’t make it a controversy</p>
<p>How about this, it does equal 1 if you can accept it.</p>
<p>1/3 = .33333
2/3 = .66667
3/3 = 1</p>
<p>Therefore, the .99999 = 1.</p>
<p>Case CLOSED.</p>
<p>1/3 = 0.33333…
(1/3)<em>3 = 0.33333…</em>3
1 = 0.99999…</p>
<p>HOWEVER, 1/3 = 0.33333… this expression on the right seems to me that it APPROACHES to 1/3 but its not exactly 1/3 theoretically. Seems to me that:
0.33333… = limit (as A approaches to infinity) sigma(from n=1 to n=A) (3/10^n)
so
0.99999… = limit (as A approaches to infinity) sigma(from n=1 to n=A) (9/10^n)
as all theoretical mathematicians should know the limit from the right side is not necessarily equal to the left side, but it APPROACHES to it.</p>
<p>Practically, 1 = 0.99999…
Theoretically, it’s not supposed to if we consider the definition of the limit</p>
<p>I agree with systemshock, 1/3 does not equal .333333, it’s just really close. But i don’t get how this works:</p>
<p>x = 0.9999999…
10x = 9.999999…
10x - x = 9.999… - .9999999…
9x = 9
x = 1</p>
<p>It’s so simple but why does it work. gaah</p>
<p>Norris212, I think Auburnmathtutor already answered your current question in the previous page:
"Close, soggy_daisy, but…</p>
<p>x = 0.999…
10x = 9.999…0
10x - x = 9.999…0 - 0.999…
9x = 8.999…81
x = 0.999…</p>
<p>By the way, the notation x.xxx…x means “an infinite number of whatevers, ending with a whatever.” I know that totally blew your mind. "</p>
<p>and I agree with him, x = 0.9999999… Let’s say the number of nines is N. If you multiply x by 10 you move up one decimal place, but you have the name number of nines (N) so you end up with a “0” at the end (if you want 10x and x to have the same amount of decimal places):
x = 0.9999…999 and 10x = 9.9999…990.
so 10x - x = 8.9999…991
so x =/= 1
and remember those 2 "x"s are equal so they must have the same number of nines even if they approach to infinity, thats why i said theres a N number of nines, we dont know how much is N but we do know the number of nines wont change if you multiply it by 10.</p>
<p>auburnmathtutor has stated that the post he made “proving” 0.999… =/= 1 is a joke.</p>
<p>systemshock: The number of nines is infinite. As in, infinite. As in, there is no zero at the “end” of it because there is no end. In your example, N is not a well-defined number. In fact, it is not a number at all, it is infinite.</p>
<p>0.3333… is the decimal notation for 1/3. They represent the exact same number, the same way 2/3 and 4/6 represent the exact same number. Not convinced? Try it in base 9. 10/3 is 3 in base nine, while 10/4 is 0.44444…</p>
<p>Apparently it didn’t sink in, so I’ll say it again: the concept of 0.999… is possible only when considered as a limit. It continues on infinitely. You cannot write it out or measure it because it is a LIMIT.</p>
<p>But hawkings, x = x, so they must have the same number of nines no matter how infinite they are, thats why I said theres an N amount of nines for “x”, which i have no idea what it is but it goes on forever.
(A calculator is never accurate, its just precise, you can ask any computer scientist, after all its like a computer and computers can only perform addition in terms of mathematics) another thing 0.33333… only approaches to 1/3. Because the notation of 0.33333… is more like expressed as an infinite series of 3/10^n where n = 1,2,3,4,…A where A approaches to infinity. And you know infinite series is still a limit so no matter how many decimals there are it will never be exactly 1/3 because it will go on forever rather it approaches to it. Otherwise how many decimals do u think there should be in order to be 1/3. Now, even if those two x’s dont have an N amount of nines, then the proof will still be wrong, because their substractions would not be defined or that 10x - x =/= 9.999…999…, rather 10x - x = 9.9999…#@$(@… All I’m saying is that that proof is wrong either way</p>