<p>lets see.
1/9=.111111....
2/9=.222222....
3/9=.333333....
...
7/9=.777777....
8/9=.888888....
9/9=.999, er... i mean 1.</p>
<p>so yes. they are equal.</p>
<p>and that's what i'll keep telling myself too.</p>
<p>I can't do this high level math but isn't this kind of like nuclear half life? the radiation gets less and less but never goes away completely because it can't reach zero?</p>
<p>yes => .99999...= 1
the proof just requires some simple algebra...</p>
<p>Assume:
.99999...= x</p>
<p>9.99999=10x
9.99999... -.9999... = 10x- .999999.... = 10x -x
9 = 9x
x= 9/9 = 1</p>
<p>
[quote]
That example ^ really wasn't what he/she was doing, but yes to assume is to make an A$$ out of U and ME (assume in capital letters, nifty huh....ok not cool at all.)
[/quote]
</p>
<p>No, it is what they were doing, just the difference between 1/3 and .333 was exaggerated with 2 and 4.</p>
<p>The fact is .999 does not = 1.</p>
<p>Look at a graph of f(x)= 1/(x-1)
Notice that as x APPROACHES 1, f(x) APPROACHES (but never hits) infinity</p>
<p>This is the exact same concept here. As we increase the decimal places, .999... APPROACHES (but never hits) 1.</p>
<p>"A is A"</p>
<p>
[quote]
yes => .99999...= 1
the proof just requires some simple algebra...</p>
<p>Assume:
.99999...= x</p>
<p>9.99999=10x
9.99999... -.9999... = 10x- .999999.... = 10x -x
9 = 9x
x= 9/9 = 1
[/quote]
</p>
<p>SO WRONG!</p>
<p>here is what you were trying to show:</p>
<p>Assume:
.9999=x
9.999=10x (NOTICE THERE IS ONE LESS DECIMAL PLACE, THIS TYPICALLY HAPPENS WHEN YOU MULTIPLY BY 10)
9.999 - .999 = 10x - .999
9 = 10x -.999
9.999 = 10x
(divide by 10) .9999 = 1
This applies no matter how far you extend the decimals, because 10x is always going to be one less decimal, it is undeniable.</p>
<p>you are wrong! .999... never equals one. At least give some better proofs than these crackpot ones.</p>
<p>
[quote]
f(x) APPROACHES (but never hits) infinity
[/quote]
exactly.
it can never HIT infinity.
but ".999...." does extend to infinity (even though we can't quantify it)
there is a world of difference</p>
<p><a href="NOTICE%20THERE%20IS%20ONE%20LESS%20DECIMAL%20PLACE,%20THIS%20TYPICALLY%20HAPPENS%20WHEN%20YOU%20MULTIPLY%20BY%2010">quote</a>
[/quote]
</p>
<p>there is NOT one less decimal place because .999... extends to infinity! obviously .999 does not equal 1, BUT .999... DOES</p>
<p>No, there is no difference, it is the exact same thing. Just like with limits we can get closer and closer to the value that can't exist, but we can never hit the value itself.</p>
<p>If x approaches 1, it is never equal to one, it is simple as that.</p>
<p>And please respond to my correcting your "simple algebra"</p>
<p>
[quote]
No, there is no difference, it is the exact same thing. Just like with limits we can get closer and closer to the value that can't exist, but we can never hit the value itself.
[/quote]
just because we can't quantify infinity does not mean it can't exist.</p>
<p>
[quote]
If x approaches 1, it is never equal to one, it is simple as that.
[/quote]
what?</p>
<p>so
lim as x approaches 2 of (x-2)/5 = 0
therefore (x-2)/5 can't = 0?</p>
<p>
[quote]
This applies no matter how far you extend the decimals, because 10x is always going to be one less decimal, it is undeniable.
[/quote]
no there won't.
All you do when you multiply by 10 is move the decimal point over one space to the right. </p>
<p>.9990 * 10 = 9.990
BUT in .999..., the nines extend to infinity, so instead of 0 at the end, you'll have 9.</p>
<p>That is a different type of limit than we are talking about. </p>
<p>Why don't we get a Caltech or MIT student in here and see what they say.</p>
<p>
[quote]
That is a different type of limit than we are talking about.
[/quote]
</p>
<p>what is a different type of limit than we're talking about?
the ONLY difference is that 2 is quantifiable and infinity is not. You're saying that because you don't know what infinity is, you can't manipulate in algebraic problems.</p>
<p>you don't need a caltech or mit student to do this.</p>
<p>Okay look, you aren't looking at this the right way. We have to use the same number of decimal places for x in x and 10x. You cannot use .99 for x in the case of x, and then .999 for x in the case of 10x. It is that simple. It is stupid to argue this point because you can always say "oh well it goes out to infinity, so you can do whatever you want." Well then you could also use .9 for x in the case of x and then .999 for x in the case of 100x, and then 9 for x in the case of x and then .999 for x in the case of 1000x, and etc. </p>
<p>The fact is, they are not equal.</p>
<p>"..." means it extends forever. but yeah...it extends to infinity therefore you can "do whatever".
infinity is a theoretical concept. In theory the numbers would go on forever even if you can't picture it in reality</p>
<p>you haven't done series have you? you can prove it using series too.. one of the other posters alluded to that.</p>
<p>I actually have, stop being a condescending *******. I have taken AP Calc BC and am probably just as experienced in math as you. Yeah obviously an INFINITE series of that is going to APPROACH one.</p>
<p>I will say it once again, A is A.</p>
<p>.999... will always need to have .00...1 added to it in order to equal one. It is always missing a small part that also approaches zero, just as .999... approaches one.</p>
<p>
[quote]
I actually have, stop being a condescending *******. I have taken AP Calc BC and am probably just as experienced in math as you. Yeah obviously an INFINITE series of that is going to APPROACH one.
[/quote]
</p>
<p>you started with the condescending bs, I was just retaliating. "give me a better proof than this crackpot one", "none of you who say .999...=1 are using any real logic", etc.</p>
<p>
[quote]
I will say it once again, A is A.
[/quote]
2+2 = 4
just because it looks different doesn't mean it's not the same thing.</p>
<p>another poster said that 1/3 = .333...
therefore:
1/3 +1/3 +1/3 = .333... +.333... +.333...
3/3 = .999...
1 = .999...</p>
<p>or does 1/3 not equal .333...? </p>
<p>You're response was :
well, that's all just an assumption.</p>
<p>The problem is, since essentially all of math is theory and only a small portion of it can be verified in reality, wouldn't everything beyond basic arithmethic be an assumption?</p>
<p>I'd be real careful multiplying, dividing, adding and subtracting infinite decimals. I think the math principles shown to "prove .999..." = 1 are pretty shaky at best. My opinion, .999... approaches but never equals 1.</p>
<p>Also, 3/3 is 1, not .999.... 3<em>(1/3) is also 1. 3</em>.333... is another story, and I believe that distinction might be what we're missing.</p>
<p>wow ...i dont really get all thes calculations but i it seems like .9999999999999 to whatever would never get to one. I wonder do numbers really exist? Is math something we made up to explain the world like the greeks made up the gods? and time...does it exist? isn't it just our description of what it takes to get from here to there? mathematical time doesn't exist, time is only literary. life is only a series of snapshots.</p>
<p>most of math is basically something we made up because it's based on a number of assumptions - like all theories.
My opinion is that we ought at least to be consistent with those assumptions. If we assume that .999... can extend forever and ever into infinity, then, in order to be consistent with that assumption, moving the decimal point over one would not change the number of 9s to the right of the decimal point. This is because the number would still extend forever and ever into inifnity. If we assume there is one less 9 to the right of the decimal point, we assume that .999... is finite; that is, we would be assuming that at some unquantifiable point, the nines turn themselves into zeros. I think that's a little arbitrary and it's not consistent with the original assumption that the nines extend to infinity. If we assume that .999... means that the number extends so far out that it's not possible to imagine it's size, but that it is still a finite number, then i would agree .999... would not equal 1.</p>
<p>As for time - I think it exists, but we're not able to understand it without relating it to the other dimensions. I think that's true of all the dimensions though. What do we define as depth if we can't relate it to length and width?</p>
<p>human beings are different from animals partly in our ability to use and manipulate symbols... numbers are one of our more powerful symbols (i'd put only language ahead of it). As for time... well, no one really understands how we experience time. </p>
<p>As for the original intent of this post, I say they equal. I use the 1/3 etc etc argument... what do you have to be smoking and in what quantity to get 1/3 as equal to any other decimal than .33333...? </p>
<p>Atomicfusion, do you really beleive that A is A? When you divide 1 by 3 and get 34.265, A is not really looking so... well, A-esque. Might as well say "A is X." Aristotle just may be rolling over in his metaphysical, non-contradictory grave...</p>