I've a question: is 0.(9) the number 0.9999 followed by an infinity of nines or is it the limit of that? If it's the limit then it's equal to 1, if not, it's not 1. (this notation isn't used in france - I supposed it was the former) <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> The limit of what?
I was taught that 0.9_ equals 1 by my math professor also.
You see, the 0.00...01 number itself is not there. There's no such number. There's a reason It's called repeating number. You starts with 0, you ends with 0. My professor basically use it to somewhat prove 0.9_ equals 1.
<!--QuoteBegin-FireStorm+Jul 11 2004, 10:57 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (FireStorm @ Jul 11 2004, 10:57 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> the limit of "the number when the number of nines goes to infinity"
basically (maple syntax) limit(sum(9/10^n,n=1..x),x=infinity); <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> If its a number, its not a limit
But yes, i meant 0.(9) = limit(sum(9/10^n,n=1..x),x=infinity);
ah ok, then it's a limit. I thought it was just zero dot infinity of nines. but yeah if it's a limit then it's 1 because limit(sum(9/10^n,n=1..x),x=infinity) = 1
by the way in this case the limit is a number. did you expect a matrix or what?
<!--QuoteBegin-FireStorm+Jul 11 2004, 11:07 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (FireStorm @ Jul 11 2004, 11:07 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin--> ah ok, then it's a limit. I thought it was just zero dot infinity of nines. but yeah if it's a limit then it's 1 because limit(sum(9/10^n,n=1..x),x=infinity) = 1
by the way in this case the limit is a number. did you expect a matrix or what? <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd--> It's the same as zero dot infinity of nines if you write down limit(sum(9/10^n,n=1..x),x=infinity) you'll se it is.
Seeing that this basically pans out to be a <a href='http://www.unknownworlds.com/forums/index.php?showtopic=73551&st=135' target='_blank'>double thread</a> (posted by the same person, no less), I'll go ahead and <span style='color:red'>***lock***</span> it.
coilAmateur pirate. Professional monkey. All pance.Join Date: 2002-04-12Member: 424Members, NS1 Playtester, Contributor
edited July 2004
<!--QuoteBegin-handeh+Jul 11 2004, 08:22 AM--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (handeh @ Jul 11 2004, 08:22 AM)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->BTW in the original 1=0.(9) conversation i found ziggy said this:
these are the lecture notes from the first semester reasoning course of my first year at university, infinite decimals are explained on page 30 (chapter 16) enjoy. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
You people ought to check it out, you might learn something new.<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd--> To add to Nem's comment, the above link is a good one to check out. In mathematical theory, yes, 0.(9) does equal 1.(0). In the real world, as you cannot measure 0.(9), the two are effectively different numbers.
As others have said, 64 != 65. The image is an optical illusion and the imprecision of the angles can be seen if you look closely.
As for this, <!--QuoteBegin-I Gorged Your Mom+--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->You are all falling into my trap. I did not make this thread to discuss if 64=65. I made it to talk about 1=.99. If you notice, in my first post I had said that everyone agrees that 1=.99. This was bound to upset some people, and make them start talking about that thread instead, which is much more interesting and fun to watch people get angry over.<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Comments
I've a question: is 0.(9) the number 0.9999 followed by an infinity of nines or is it the limit of that? If it's the limit then it's equal to 1, if not, it's not 1.
(this notation isn't used in france - I supposed it was the former) <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
The limit of what?
Yes, semester.
You see, the 0.00...01 number itself is not there. There's no such number. There's a reason It's called repeating number. You starts with 0, you ends with 0. My professor basically use it to somewhat prove 0.9_ equals 1.
basically (maple syntax) limit(sum(9/10^n,n=1..x),x=infinity);
basically (maple syntax) limit(sum(9/10^n,n=1..x),x=infinity); <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
If its a number, its not a limit
But yes, i meant 0.(9) = limit(sum(9/10^n,n=1..x),x=infinity);
by the way in this case the limit is a number. did you expect a matrix or what?
but you still posted <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html//emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif' /><!--endemo-->
by the way in this case the limit is a number. did you expect a matrix or what? <!--QuoteEnd--> </td></tr></table><div class='postcolor'> <!--QuoteEEnd-->
It's the same as zero dot infinity of nines if you write down limit(sum(9/10^n,n=1..x),x=infinity) you'll se it is.
Why would i expect a matrix?
<!--QuoteBegin--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->http://www.ma.man.ac.uk/~grant/notes03.pdf
these are the lecture notes from the first semester reasoning course of my first year at university, infinite decimals are explained on page 30 (chapter 16) enjoy. <!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
You people ought to check it out, you might learn something new.<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
To add to Nem's comment, the above link is a good one to check out. In mathematical theory, yes, 0.(9) does equal 1.(0). In the real world, as you cannot measure 0.(9), the two are effectively different numbers.
As others have said, 64 != 65. The image is an optical illusion and the imprecision of the angles can be seen if you look closely.
As for this,
<!--QuoteBegin-I Gorged Your Mom+--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> (I Gorged Your Mom)</td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->You are all falling into my trap. I did not make this thread to discuss if 64=65. I made it to talk about 1=.99. If you notice, in my first post I had said that everyone agrees that 1=.99. This was bound to upset some people, and make them start talking about that thread instead, which is much more interesting and fun to watch people get angry over.<!--QuoteEnd--></td></tr></table><div class='postcolor'><!--QuoteEEnd-->
Do it again and you won't.