no, if he's right then he's right 1/3 =.3333333333... that's a given 3 * .3 =.9 3 * .33 =.99 3 * .333 =.999 ... 3*.333recurring=.9999recurring 3*(1/3)=.9999recurring here's the algebraic proof placed into some calcusu based terms lim(m --> ∞) sum(n = 1)^m (9)/(10^n) = 1 0.9999... = 1 Thus x = 0.9999... 10x = 9.9999... 10x - x = 9.9999... - 0.9999... 9x = 9 x = 1. of course since people here fail to understand the arithmetic proof, and the algebraic proof just goes over their head this probably won't do much... and here is a geometric proof of it as defined by a series http://www.physicsforums.com/latex_images/67/678504-0.png and here's a very simple calc proof 1[-1/(10^∞)]=.9999999999(recurring) so basically 1/(10^∞) would be a decimal with a lot of 0s and a 1 at the end right? lim x ->∞ 1/(10^x)=0 nope? it's 0. 1 divided by ∞=0
You throw a rock at a dude's car. You don't hit dead center on the window...but it still breaks. 0.9 repeating isn't 1...but it's close enough for it to count
no it's 1. if you're doing a greatest interger function and you end up with .9recurring as the independant variable and you so for f=[[x]] f(.9recurring)=1 that's right it equals 1. if it didn't equal 1 then f(.9recurring) would equal 0. there IS mathematical significance to this. in most cases it doesn't matter but there are some cases. If you get a dick of a professor and they include a question like the above on a test, expect a 0 if your answer is 0. it can matter f=tan π/(2*[[x]]) in that case your definition is the difference between "0" and "undefined" that's what I get for having a major which requires 3 semesters of upper level calculus and stats...
that might be the case, but it still doesn't mean that you're any more knowledgeable on the matter. chances are you're not. especially if you don't accept fundamental aspects of math
divide 1/3 manually by hand in the standard 10 digit decimal system it does if that doesn't work for you then 1/7=.1428571428... +6/7=0.857142857... =9/9=.99999999999... 1/6=.1666666666... +5/6=0.833333333... =6/6=.99999999999... it's true for ANY rational expression FYI.
i don't know what is said on page 2-4, but it's nothing more than complete bull----. i believe with "repeating" you mean an infinite amount. so 0.9999(repeating) would be nothing more then a zero, a dot and then an infinite amount of 9's. Whenever you multiply that by 10, you will get a 0 at the end, no matter how many 9's there are behind the dot, you will never end up with a 9 at the end. That being true, the rest of the calculation is just garbage. So .99999 equals 1 is false unless you start to round off. The correct math thingy: x=0.99~9 (~ stands for a lot of the same) 1.) So that would mean that 10x = 9.99~90 2.) 10x - x = 8,999~91 (9.99~90 - .999~9 = 8,999~91) 3.) so 9x = 8,999~91 4.) Which means x = 0,99~9 once it is reduced!