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| Post Info | TOPIC: 0.999999' equals 1 |
| Posted By: Bruno Posted On: May 22, 2007 Views: 1173 | 0.999999' equals 1 Oh my ... sorry, I don't want to offend anyone by starting a new discussion on this one, I just have to write *something* after reading that topic. Anyway, if I had ANY reason what so ever, to feel stupid in posting my theory here a while ago, I have to admit that it's nothing after reading that topic about that 0.9999' equals 1. I almost fell off the chair, so amused was I by reading it! I'm amazed, that anyone can even try to prove that these numbers are equal. But very amusing reading, anyway! lol |
| Posted By: Keith Mayes Posted On: May 25, 2007 Views: 1163 | RE: 0.999999' equals 1 Don't even go there. There are a lot of very clever mathematicians who can 'prove' that 0.999' does equal 1. However, I disagree. 0.anything is less then 1. They are being too smart for their own good. |
| Posted By: Bruno Posted On: May 26, 2007 Views: 1159 | RE: 0.999999' equals 1 Yes, I agree with you...not worth getting into that discussion with them :-/ lol |
| Posted By: Charles Matthew Posted On: Sep 21, 2007 Views: 1063 | RE: 0.999999' equals 1 At first I was pretty damn confused by this, but then I read the wikkipedia article on the topic. It pretty much showed me what I expected. That is, this isn't really an argument about logic, but semantics. All it means is that there are more ways than one to represent "1." To be honest, it seems a rather paltry mathematical argument, but then, I probably lack a comprehensive understanding of the topic since I've never encountered a 0.999 repeating decimal in any class that I've ever taken. Is it actually possible to get that result in an equation that manipulates real, quantifiable values? I suppose the answer is yes. Because 1 divided by 1 would yield it. As would many other equations. You wouldn't get 0.999 repeating on a calculator, but that's just because whoever programmed the thing chose to represent the quantity of "one" with a "1" rather than 0.999... and so on. Thus, as far as I can tell, it really IS just about semantics. But then, I have much to learn. In any case, the question that struck the point home for me is this: What fractional part of "1" is "0.999..." repeating? What would you multiply it by to get "1"? You can multiply other repeating decimals by a number and get "1". 0.333.. repeating for instance. Yet, 0.999 repeating, when multiplied by ANYTHING less than or greater than "1" will give you something other than "1". In other words, it isn't a fractional part of "1", it IS "1". Still, isn't this a pretty useless point? Maybe it isn't. If somebody can link me to page with some sort of practical application I'd appreciate it. |
| Posted By: Keith Mayes Posted On: Sep 21, 2007 Views: 1060 | RE: 0.999999' equals 1 Yes, it is about semantics. As for a practical application, no, never come across one. I find it strange though that mathematicians contradict mathematics. By starting a number with 0.(anything) then that is clearly saying the number is less than one. Then they say no it isn't. Seems strange to me. Maybe its just me. |
| Posted By: deepak Posted On: Jul 26, 2008 Views: 839 | RE: 0.999999' equals 1 No,its not true anything less than one can not be equals to one question have no point. |
| Posted By: YoDummies Posted On: Sep 3, 2008 Views: 814 | RE: RE: RE: 0.999999' equals 1 Ok it's really quite simple...LOOK: Step 1) .9999(repeating) = x ~ That's our equation. Step 2) Multiply both sides by ten. ~ 9.999(repeating) = 10x Step 3) Subtract our first equation from our second. _________________________ 9.999(repeating) = 10x - .999(repeating) = x ------------------------- Step 4) We are left with: 9 = 9x Step 5) Simplify -> and therefore x = 1! *When you subtract a repeating decimal (A) from another repeating decimal (A) you are left with zero. That process illustrates why .999(repeating) is in fact equal to one. The proof is there! No arguments please. |
| Posted By: Keith Mayes Posted On: Sep 3, 2008 Views: 811 | RE: 0.999999' equals 1 Thanks but we have discussed that equation many, many times. It is not possible to multiply a number that is infinite in length, in fact you can't do anything with it, this is not an opinion, its how maths works. As an example what do you calculate 3 x 0.999' to be? Its for sure not 3. Also the argument that 0.9999' = 1 is flawed right from the start. Take the sequence -3, -2, -1, 0, +1, +2 +3 Any number to the left of a number is less than, any number to the right is greater than, that is how maths was constructed, its a basic fact of mathematics and is unarguable. It is therefore obvious that 0, or 0.anything, is less than 1 as it is to the left of it. That is why we use the zero, it signifies zero, less than 1. Its that simple. All the daft arguments that say different are nothing more that trying to change the original value of the mathematical numbers, what is the point in that? |
| Posted By: YoDummies Posted On: Sep 4, 2008 Views: 806 | RE: 0.999999' equals 1 "It is not possible to multiply a number that is infinite in length" -You can't multiply a number that is infinite in length? An 'irrational number' is synonymous with an 'infinite number' is it not? For example take the fraction 1/3. That is an irrational number. It is equivalent to .3333(repeating). We can easily multiply this fraction by two if we wanted. Therefore your statement is incorrect. We CAN in fact multiply an infinite (irrational) number. We do it all the time in math! Keith think about this: 1/3 + 1/3 = 2/3 = .666' .333' + .333' = .666' 1/3 + 1/3 + 1/3 = 3/3 = 1 .333' + .333' + .333' = .999' Therefore, 1 = .999' |
| Posted By: Yo Dummies Posted On: Sep 4, 2008 Views: 803 | RE: 0.999999' equals 1 Ok, I just spent some time looking through some previous posts (which I should have done earlier), and I can bet I know what your response will be Keith. You'll argue that 1/3 cannot be equally expressed as a decimal. Ok fine. Then let's look at it using your own example: You say .999' is less than 1 on a simple number line right? That seems like basic math. Ok. Well let me ask this...What can I add to .999' to get a sum of one? You could argue that you cannot add anything to a number that continues forever. Hmm. Well then does a number that continues infinitely actually exist? Is there a number that is greater than .999' yet less than 1? There has to be if we assume .999' exists right? |
| Posted By: Bruno Posted On: Sep 5, 2008 Views: 797 | RE: 0.999999' equals 1 YoDummies says, that 1/3 equals .333', so that .333' * 3 equals 1. This is incorrect. 1/3 does NOT equal .333' - this is only an approximation, since .333' goes on forever without ever becoming equal to 1/3 - at it's best, it will always be an approximation, and ONLY an approximation. Nor will .999' ever be equal to 1, no matter how many digits you add. Can it really be that difficult to see the logic in that? |
| Posted By: obx Posted On: Nov 22, 2008 Views: 751 | RE: 0.999999' equals 1 If you approach numbers rationally then "lim x->1 = 1" so 0,999' = 1. (Or 1/3 = 0,333' -> 0,333' * 3 = 0,999') But if you define 0,999' as an infinite complex number (irrational, like pi), then 0,999' < 1. :-) Mathematics and numbers are just instruments to examine concepts in our nature. A number has a value depending on the set you use in the frame of numbers, they are not absolute. So you shouldn't take them too seriously. free your mind. |