Union 5-3992 Posted July 31, 2015 Author Share Posted July 31, 2015 Decimals are used as approximations of fractions, not necessarily the true value. I disagree. The decimal fraction is a type of notation - not an approximation. One-third, 1/3, and 0.33333333....(3's repeating forever) are all exactly the same number. They are just written in different notations. Just because we cannot fully express the value of 1/3 in decimal fraction notation does not mean that the number is different. All it means is that we are physically unable to write down an infinite number of 3's, so we use a shorthand notation. The same goes for any rational number's denominator that has prime factors other than 2 or 5....for example, 1/7. The decimal fraction notation for 1/7 is 0.142857142857......(infinitely repeating sequence of 142857), but it is still the exact same number as 1/7. We're just writing it differently. Mathematicians have proven 0.999999...to be equal to 1. They've proven it algebraically (like I did in this thread), via infinite series and sequences, and via other methods. The "paradox" is merely the common skepticism that students have when first addressing the issue. At first look, it is counterintuitive to say that 0.999999....equals 1. However, when actually doing the math, we find that they are indeed equal. And 6 x 0.1666666666......(ad infinitum) equals 0.9999999999999..........(ad infinitum). There is no 6 to the right of all the 9's, as there are an infinite number of 9's. We cannot put anything at the end of an infinite sequence. We'll never catch it!I wasn't stating what I originally wrote as fact, I just wanted to see folks debate/discuss it. You won though Link to comment Share on other sites More sharing options...
Principled Man Posted July 31, 2015 Share Posted July 31, 2015 I just wanted to see folks debate/discuss it. Here at The Rush Forum, we can discuss-debate-argue-spoof anything and everything! We are relentless..... :laughing guy: :laughing guy: 1 Link to comment Share on other sites More sharing options...
HemiBeers Posted July 31, 2015 Share Posted July 31, 2015 Good enough to me. When infinity finally comes to an end, it's going to have some explaining to do. as a programmer part of the time, i usually just round that shit to 2 decimal places. Life would be much simplier if all insignificant shit could be rounded and forgotten. Canada is doing that. Financial transactions are rounded to the nearest five cents so you no longer have to deal with pennies. damn canadiens are so pragmatic. Costs more to make a penny than it's worth. They would cry 'socialism' if we tried that in the U.S. Link to comment Share on other sites More sharing options...
HemiBeers Posted July 31, 2015 Share Posted July 31, 2015 Decimals are used as approximations of fractions, not necessarily the true value. I disagree. The decimal fraction is a type of notation - not an approximation. One-third, 1/3, and 0.33333333....(3's repeating forever) are all exactly the same number. They are just written in different notations. Just because we cannot fully express the value of 1/3 in decimal fraction notation does not mean that the number is different. All it means is that we are physically unable to write down an infinite number of 3's, so we use a shorthand notation. The same goes for any rational number's denominator that has prime factors other than 2 or 5....for example, 1/7. The decimal fraction notation for 1/7 is 0.142857142857......(infinitely repeating sequence of 142857), but it is still the exact same number as 1/7. We're just writing it differently. Mathematicians have proven 0.999999...to be equal to 1. They've proven it algebraically (like I did in this thread), via infinite series and sequences, and via other methods. The "paradox" is merely the common skepticism that students have when first addressing the issue. At first look, it is counterintuitive to say that 0.999999....equals 1. However, when actually doing the math, we find that they are indeed equal. And 6 x 0.1666666666......(ad infinitum) equals 0.9999999999999..........(ad infinitum). There is no 6 to the right of all the 9's, as there are an infinite number of 9's. We cannot put anything at the end of an infinite sequence. We'll never catch it!Dude...this ^^^^^ proves you're the very definition of nerd. Wear the badge with honor my friend. Seriously, I got an erection from reading that explanation. Math rarely does that for me :outtahere: 1 Link to comment Share on other sites More sharing options...
Crimsonmistymemory Posted July 31, 2015 Share Posted July 31, 2015 (edited) Oh I get it it now I was looking at the numbers in the wrong time slot.3.14 must indicate Pizza pie which is mainly for dinner (or supper as some would say). When fruit pies are primarily for dessert unless trumped if one has the munchies. Thanks to all who contributed to this thread so I may gain true understanding of the inner workings of mathmatics. Edited July 31, 2015 by Crimsonmistymemory Link to comment Share on other sites More sharing options...
blueschica Posted July 31, 2015 Share Posted July 31, 2015 Decimals are used as approximations of fractions, not necessarily the true value. I disagree. The decimal fraction is a type of notation - not an approximation. One-third, 1/3, and 0.33333333....(3's repeating forever) are all exactly the same number. They are just written in different notations. Just because we cannot fully express the value of 1/3 in decimal fraction notation does not mean that the number is different. All it means is that we are physically unable to write down an infinite number of 3's, so we use a shorthand notation. The same goes for any rational number's denominator that has prime factors other than 2 or 5....for example, 1/7. The decimal fraction notation for 1/7 is 0.142857142857......(infinitely repeating sequence of 142857), but it is still the exact same number as 1/7. We're just writing it differently. Mathematicians have proven 0.999999...to be equal to 1. They've proven it algebraically (like I did in this thread), via infinite series and sequences, and via other methods. The "paradox" is merely the common skepticism that students have when first addressing the issue. At first look, it is counterintuitive to say that 0.999999....equals 1. However, when actually doing the math, we find that they are indeed equal. And 6 x 0.1666666666......(ad infinitum) equals 0.9999999999999..........(ad infinitum). There is no 6 to the right of all the 9's, as there are an infinite number of 9's. We cannot put anything at the end of an infinite sequence. We'll never catch it! THANK YOU for explaining this correctly!! Poor math/science explanations drive me nuts! :D Link to comment Share on other sites More sharing options...
goose Posted July 31, 2015 Share Posted July 31, 2015 I just wanted to see folks debate/discuss it. Here at The Rush Forum, we can discuss-debate-argue-spoof anything and everything! We are relentless..... :laughing guy: :laughing guy: Link to comment Share on other sites More sharing options...
goose Posted July 31, 2015 Share Posted July 31, 2015 Decimals are used as approximations of fractions, not necessarily the true value. I disagree. The decimal fraction is a type of notation - not an approximation. One-third, 1/3, and 0.33333333....(3's repeating forever) are all exactly the same number. They are just written in different notations. Just because we cannot fully express the value of 1/3 in decimal fraction notation does not mean that the number is different. All it means is that we are physically unable to write down an infinite number of 3's, so we use a shorthand notation. The same goes for any rational number's denominator that has prime factors other than 2 or 5....for example, 1/7. The decimal fraction notation for 1/7 is 0.142857142857......(infinitely repeating sequence of 142857), but it is still the exact same number as 1/7. We're just writing it differently. Mathematicians have proven 0.999999...to be equal to 1. They've proven it algebraically (like I did in this thread), via infinite series and sequences, and via other methods. The "paradox" is merely the common skepticism that students have when first addressing the issue. At first look, it is counterintuitive to say that 0.999999....equals 1. However, when actually doing the math, we find that they are indeed equal. And 6 x 0.1666666666......(ad infinitum) equals 0.9999999999999..........(ad infinitum). There is no 6 to the right of all the 9's, as there are an infinite number of 9's. We cannot put anything at the end of an infinite sequence. We'll never catch it!Yeah, you are dead right about this. My assertion of the approximation argument was in the interest of flushing out TRF's resident King Dork. Your post represents your having pulled the sword from the stone. All hail the King! :hail: You know what this means........the Administrators will have to now give me a new Member Title! Suggestions: His Royal High-On-Math-Ness King Of The Dorks Mathematical Porn Star :gumby: Make it so!!! Link to comment Share on other sites More sharing options...
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