You are not a mathematician, and practices ... --------------- You are confusing two different things ... What you use is called in mathematics and physics "calculation error" ... --------------- What it is? Any object can be calculated with an error margin .. (Sorry, I'm going to use the European and Soviet system of calculation, not American For example.. - Do you use an ordinary ruler, then the margin of error - 1 mm - You are using a caliper, then the margin of error - 0.1 mm - Do you use an electronic caliper, then the margin of error - 0.01 mm .... -------------------------------------------------- ------------- For the issue before us is not relevant .... The numbers in mathematics - a theory ================================================= Now consider your data ... This is called "calculation error" When you are in the future, will produce a calculation error, it will accumulate ... But in Mathematics and in Physics have the solution ... The fact that the "calculation error" can be calculated, if you have the formula for future calculations ... More I will not write ... This task is part of the 1st course students in the USSR ... I can give examples: You measured the length of articles with an error .. calipers .. In the following: Error increases: - 2 times, if a simple linear formula - 4 times, if the quadratic formula ... Sorry, an error calculation is included in the concept of "differential calculus", so I will not have to download ... ================================= In mathematics there is no error .. ' Teach math!
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You have to define "..." or else this problem is meaningless. Of course "..." refers to the limit of a sequence. Therefore it's obvious that 1 = .99999...
And this is why mathematicians are hard to work with. Luckily I only have to worry about the statisticians. It's a pointless question. For almost any measurement you make, the two will be indistinguishable due to imprecision of measurement. However, unless you're saying the 9s infinitely repeat, they are not theoretically equivalent. .99999 with a billion 9s is not quite 3/3. Only an infinite number of 9s is. And you didn't clarify whether that is what you meant by "and so on"
Rounding up has to take place at some point to make them equal. For 1/3 never actually stops repeating. If one wants to be completely technical.
So I win $100 from you in one of your threads, your bet, and they closed the thread? Are you still going to donate the $100 to PF on my behalf?
OK....look.....when I am able to have observation time on a LART...Large Array Radio Telescope and I am turning the dishes to point at a 1 Micron are of the sky.....if I am off by 0.999999999 of a Micron.....GUESS WHAT??? I am NOT going to be able to observe what and where I want!! The fact is in any PRACTICAL APPLICATION.....0.999999999<1.0. AA
This is why you make crappy aircraft in Russia because you believe .9 and 1 are the same. One is a whole number and the other is a fraction of a whole number hence they aren't the same.
The guy thinks kids don't know how to round up..... Yeah they taught us how to round up when I was 7 - apparently they teach rounding up at 14 in Russia.
A=1 B= .500000000000000000000000000000000000000000000000000000000000000000000001 Are those the same numbers? We Americans learn this when we're 7. Oh BTW, I love how you used 1 and then you used 0.9 ..... Are you from one of those cultures that doesn't acknowledge the concept of ZERO?
Technically no, since the value is not really 1, even if only by the tiniest of margins. But in applied mathematics, they might as well be equivalent. Usually when I do math, I give no (*)(*)(*)(*)s about rounding anyways.
OP isn't wrong. 0.(9) IS equal to one. It's not infinitely close to one. It isn't approaching one. It IS one. Try and covert 0.(9) to a fraction and see what happens.
The OP is 100% wrong.... 0.9 is NOT 1 and it will never BE 1. 1 is a whole number and 0 (ZERO).9 is a fraction of 1. The only way 0.9 becomes 1 is if you round up... Besides don't you notice the ZERO in 0.9? No wonder why the Soviets failed so miserably at just about everything they were rounding numbers. For anything to work properly the numbers need to be precise. If you need a 2x4 that is 9 foot and 7/8ths you don't go and say well I guess a 10 footer will work....lol
He isn't saying 0.9 = 1. He's saying 0.999... (an infinite number or repeating 9s) = 1. You can prove that using basic algebra. If x = 0.(9) Then 10x = 9.(9) 10x - x = 9x 9.(9) - 0.(9) = 9 If 9x = 9 Then x = 1 There's no rounding involved, and the 0 before the decimal point is irrelevant. There are a number of mathematical proofs that demonstrate this, and it has been accepted within mathematics for a long time. You can laugh at or criticize other people for accepting this all you want, but you're the one that's wrong.
Do you know the difference between infinite and finite? 0.9 is infinite. 1. is finite. I'm sure Pi confuses the hell out of you. You do realize I have a degree and to get that degree I had to complete algebra? As a matter of fact I had to take algebra twice - once in high school and once in college.
Now you KNOW this is a stupid...."OH...I took one advanced mathematics class too many!"....trick that really has ZERO real world applications. Obviously if you have 0.9999999^infinite we state this is 1. But he did NOT state it was to the infinite. In REALITY.....0.99999999^infinite does not exist. It is a Statistical Impossibility for ANYTHING TANGIBLE to exist or have part of it measure 0.99999999^infinite. HOWEVER.....0.3333333^infinite exists as 1/3.....thus if we cut a pie into 3 pieces they are 0.333333^infinite of the whole or 1/3. If we add 1/3 + 1/3 + 1/3 = 3/3 or 1. But as a base 10 numerical system 1/3 = 0.333333^infinite in Decimals. Thus 3 x 0.3333333^infinite =0.9999999^infinite=1. But just 0.999999999.....DOES NOT EQUAL 1. You MUST denote that 0.9999999^infinite. AA
Pi isn't a rational number, 0.(9) is. So I'm not sure what one has to do with the other. "1" also has an implied digit that repeats an infinite number of times. I don't know what to tell you man. The concept that 1 = 0.(9) has been accepted by mathematicians for a long time. If you have some way of proving it doesn't, you should take it up with them. This Wikipedia page outlines a number of proofs that have been used to demonstrate the concept. https://en.m.wikipedia.org/wiki/0.999...
Again....he would not be objecting to this IF the author of this topic had typed....0.999999^infinite = 1. The author of the topic didn't. He posted 0.9999999 = 1. THAT...is incorrect. 0.9999999^infinite = 1...is correct. AA
0.9 is NOT 1..... If engineers accepted 0.9 as 1 a lot of (*)(*)(*)(*) wouldn't work. Do you realize that? Like I said you were going to have a difficult time with Pi because Pi is precise. 0.9 is precise and so is 1. Just for fun. Say some day we figure out teleportation.... What do you think would happen if only 0.9999999% of a person was teleported? because 0.9999999999% isn't the entire person now is it?
People keep referring to this as advanced or theoretical math. It isn't, it can literally be proven with basic algebra. Writing ".999..." Is a typical way of denoting an infinitely recurring digit. And of course the number exists. It exists in the same way 1 exists, or 10 to the power of 0 exists, or 37/37 exists, because they are all just different ways or writing the same number.
No, 0.9 does not equal 1, and that isn't what I'm arguing. However, 0.(9), 0.999..., however the hell you want to write it DOES equal 1. 0.9 and 0.(9) aren't the same number. The difference between 1 and 0.9999999 is 0.0000001. Why don't you tell me what the difference between 1 and 0.(9) is.
