Comments on: Mom was right http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/ Thoughts count Mon, 05 Dec 2011 22:48:50 +0000 hourly 1 http://wordpress.org/?v=3.1.3 By: Victoria Adams http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/comment-page-1/#comment-757 Victoria Adams Mon, 05 Dec 2011 22:48:50 +0000 http://www.discreteideas.com/?p=279#comment-757 Wow! This article was very helpful! Thanks for the tips! Hiring a personal tutor can definitely be very useful, I know a firm that services the greater Boston area. They are very affordable and I personally had a great experience with them. Please check their site out for more details about their in-home private tutoring services. http://thepremiertutors.org Wow! This article was very helpful! Thanks for the tips! Hiring a personal tutor can definitely be very useful, I know a firm that services the greater Boston area. They are very affordable and I personally had a great experience with them. Please check their site out for more details about their in-home private tutoring services. http://thepremiertutors.org

]]> By: studio2m http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/comment-page-1/#comment-642 studio2m Sun, 28 Aug 2011 00:59:40 +0000 http://www.discreteideas.com/?p=279#comment-642 mathematicaly speaking we can not write X=0.9999...(repeating to infinity). But we can write X=~0.999...(repeating to infinity).(i.e: X nearly equal to 0.999...). So if we rewrite your second demonstration, we have: X =~ 0.99999999… 10X =~ 9.99999999… Subtract the first row from the second: 9X = 9 Now divide both sides by 9: X = 1 then we have 1 =~ (nearly equal to) 0.999... (repeating to infinity), which is true. mathematicaly speaking we can not write X=0.9999…(repeating to infinity). But we can write X=~0.999…(repeating to infinity).(i.e: X nearly equal to 0.999…).

So if we rewrite your second demonstration, we have:
X =~ 0.99999999…
10X =~ 9.99999999…
Subtract the first row from the second: 9X = 9
Now divide both sides by 9: X = 1

then we have 1 =~ (nearly equal to) 0.999… (repeating to infinity), which is true.

]]> By: The Count http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/comment-page-1/#comment-523 The Count Mon, 06 Jun 2011 23:10:38 +0000 http://www.discreteideas.com/?p=279#comment-523 All very true. I'm in software, and recently had to tell someone "100% reliability is like infinity, it's a <em>concept</em>, not a number". All very true. I’m in software, and recently had to tell someone “100% reliability is like infinity, it’s a concept, not a number”.

]]> By: Rich http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/comment-page-1/#comment-522 Rich Mon, 06 Jun 2011 23:07:49 +0000 http://www.discreteideas.com/?p=279#comment-522 This argument is a classic, and the bottom line is that we have to accept the existence of .9 (or .3) repeating to infinity as the premise in order to agree. The problem is that .3 or .9 repeating is an approximation that approaches 1/3 or 1 depending on the level of precision that you are contemplating. Remember that infinity is a very large number, especially towards the end. I propose that .9 repeating (or any number repeating) is a human accepted shorthand to reconcile the incompatibility of base 10 numbering and dividing certain numbers by 3. We simply "know" that 1/3 is .3 repeating. The problem with infinity is that you can never actually get there. The difference between .9 repeating and 1 is that the value of 1 doesn't change as you contemplate it at different levels of precision. Infinity is to math and physics as Hitler is to politics. Once you go there you've already lost the argument. This argument is a classic, and the bottom line is that we have to accept the existence of .9 (or .3) repeating to infinity as the premise in order to agree. The problem is that .3 or .9 repeating is an approximation that approaches 1/3 or 1 depending on the level of precision that you are contemplating. Remember that infinity is a very large number, especially towards the end. I propose that .9 repeating (or any number repeating) is a human accepted shorthand to reconcile the incompatibility of base 10 numbering and dividing certain numbers by 3. We simply “know” that 1/3 is .3 repeating.

The problem with infinity is that you can never actually get there. The difference between .9 repeating and 1 is that the value of 1 doesn’t change as you contemplate it at different levels of precision. Infinity is to math and physics as Hitler is to politics. Once you go there you’ve already lost the argument.

]]> By: Fractured Memories « Discrete Ideas http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/comment-page-1/#comment-54 Fractured Memories « Discrete Ideas Sun, 04 Jul 2010 04:12:17 +0000 http://www.discreteideas.com/?p=279#comment-54 [...] That’s 0.333*, where the 3s never stop, also called 0.3 repeating. And yes, 0.9 repeating does equal 1! [...] [...] That’s 0.333*, where the 3s never stop, also called 0.3 repeating. And yes, 0.9 repeating does equal 1! [...]

]]> By: Tips for Financing Your Nursing School Education http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/comment-page-1/#comment-51 Tips for Financing Your Nursing School Education Tue, 29 Jun 2010 02:05:00 +0000 http://www.discreteideas.com/?p=279#comment-51 <strong>Graphing Calculators as a Primary Teaching Tool...</strong> it not only gives the right answers but also acts as their teaching guides... Graphing Calculators as a Primary Teaching Tool…

it not only gives the right answers but also acts as their teaching guides…

]]> By: What is a Series | Best Home Improvement tips http://www.discreteideas.com/2010/05/mom-was-right-repeating-9/comment-page-1/#comment-30 What is a Series | Best Home Improvement tips Fri, 14 May 2010 01:14:02 +0000 http://www.discreteideas.com/?p=279#comment-30 [...] Mom was right « Discrete Ideas [...] [...] Mom was right « Discrete Ideas [...]

]]>