<p>An intriguing question!</p>
<p>no....... it approaches 1</p>
<p>That's how my school did Marching Band now I get .33333333 for doing it my SR. year</p>
<p>Actually, 0.9999999 repeating does equal 1. 0.999999 repeating can be represented by an infinite geometric series.</p>
<p>0.9 + 0.09 + 0.009 + ... and so on. Using the formula, (t1)/(1-r) where t1 is the first term and r is the rate, plug in the numbers. You get:</p>
<p>0.9/1-0.1 = 0.9/0.9 = 1.</p>
<p>The reason I hate this question is that it is not a debate, it is a question of definitions. "0.999..." is not a number at all, because its digits do not end. However, it is generally conventional to DEFINE what an infinite decimal means, which is the limit of a series. Indeed, the limit in question equals 1.</p>
<p>However, one could also define a decimal to simply be a sequence of numbers, in which case 0.999... is certainly a different sequence than 1.000..., and thus they are not equal. One would have difficulty creating well-defined algebraic properties within this definition, however (example: does 0.4999...+0.5000... equal 0.999... or 1.000...? There is no way to standardize this).</p>
<p>It is interesting to note that, using this definition (which indeed is standard), all terminating decimals actually have two different decimal expansions. For example, 2/5=0.4000...=0.3999... Both are infinite decimals, and both approach the same limit value.</p>
<p>nono, 0.9999... does equal one. there are many numbers whose digits don't end, like pi and 1/7 (the first has no pattern, the second does). anyway, regardless of how you look at it, they are both numbers and 0.999... equals one. my favorite proof:</p>
<p>x=0.9999....
10x=9.999....
subtract the two equations in reverse order (it should be quite trivial to prove why you can perform any arithmetic operation with two sides of two two equations to produce a new true equation)
9x=9 (because the decimal part cancles out)
x=1
qed</p>
<p>wrong, the decimals do not cancel out because 10x will have a shifted left last digit...</p>
<p>lol, wow...</p>
<p>As for gxing's explanation. That is an incorrect way to do an infinite geometric series. In a geometric, you multiply the first term (and the subsequent terms) by the same rate. You do not add the multiplication of the original term. So an infinitie geometric series starting at .9 (for simple reasoning) would go:</p>
<p>.9, .09, .009. Not added. Simply put into terms.</p>
<p>The formula you used was an odd combination of an arithmetic and geometric series.</p>
<p>I have had to argue this point so many times with so many people... It hurts my eyes to see such a heathen conversation. .99999.... does equal to 1, there is no question. You are wrong, the mathematics community is right. And a series is in fact a sum so gxing was correct. You are thinking of a geometric sequence jaug1. The key word here is series. Look it up.</p>
<p>Ah. Misread what he had written. Never mind my comment. :)</p>
<p>0.333...+0.333...+0.333...=0.999...
0.333...=1/3
1/3+1/3+1/3=1
1=0.999...
qed</p>
<p>1/3 = 0.333..., and 3/3 = 1.
0.333... is assumed to equal 1/3, and 1/3 x 3 = 0.999 but since 3/3 = 1, 3/3 must equal 0.999... clearly!</p>
<p>For all practical purposes, .999... equals 1.</p>
<p>0.999... doesn't really equal 1, but we pretend like it does so this world makes sense and we don't all go bonkers</p>
<p>0.333...+0.333...+0.333... != 0.999...</p>
<p>Everyone is clearly defining it and giving their position, but it seems like when you write out 1/3 is equals .3333333. But, in actuality the number should be ever so slightly higher since 3/3 equals 1 as snuffles pointed out.</p>
<p>The problem is the infinite decimal that causes the conufion. If there was no infinite decimals with these numbers, everything would work out.</p>
<p>Wow, those who argue .999=1 use some of the worst, elementary, logic I have ever seen. </p>
<p>Open up your calculus book to limits and study that before you make ridiculous posts...</p>
<p>here's an example of the flawed logic I am talking about:</p>
<p>
[quote]
0.333... is assumed to equal 1/3
[/quote]
</p>
<p>So, you are proving .999=1 by making an assumption that isn't even true? That makes sense. Mathematicians tend to use TRUE statements as proof, instead of FALSE statements or "assumptions". If we wanted to make an assumption, then we would just assume .999=1 in the first place, which is the same concept as assuming .333=1/3.</p>
<p>This is basically what you are doing:
Prove 4=8
Assumption (aka false statement): 2=4
2<em>2 = 2</em>4
4 = 8
look, it works!</p>
<p>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.)</p>
<p>lol.. best question ever!</p>