A friend of mine brought this up, as it is a debate going on right now in the worlds of science and math. Basically, the argument is that a decimal fallowed by an infinite number of nines is actually equal to One.
But this is all well and good for the world of Math. But science has proven a different logic, were they are not equal. My favorite example is that in science, one plus one is approximately two, due to the impurities of one. This expression basically is stating that having two halves put back together does not make it whole again.
So in my argument, I argue that if 0.999... is equal to 1, then 1 is equal to 2. I shall demonstrate using the same logic. I shall refer to an infinite amount of numbers using "..."
There does seem to be a lot of disagreement about the OP, though. The fact that .9999 = 1 has been proven. The proof that 1 = 2 is flawed. In fact, it is a basic axiom of arithmetic that no number can equal its successor. Thus, the title of the thread is beyond debate.
because 1 whole number can never be split into 3 equal parts, splitting it would be like splitting your guitar into 3 equal parts with equal shapes, can you really do that? i dont think so.
the reason why the number is infinitely going on 3 (0.3333333333333) is because the equation is trying to look for a number which can split accurately the whole number to three... and can the equation find it? no, it cant, which is why the the process of three goes on infinitely.
this number which can accurately split the whole number into three is what we may call 'an invisible number' because it cannot be written on any sheet of paper. and as long as this 'invisible number' is not computed as part of the 0.333.... decimal, multiplying it to three will only result to a 0.99999...
you might as well rewrite the equation as 0.33x + 0.33x + 0.33x = 1 or add it by 0.33(keeps going on) + 0.33(keeps going on) + 0.33(keeps going on) = 1, which is quite impossible to do...
0.33x + 0.33x + 0.33x = 1 0.99x = 1
which once again leads to another mathematical problem with its own set of invisible another---> x=1.01(so on)
1.01 (x) ^ cannot be written as a whole, thus an invisible number is added ^
but i do not believe 0.99(so on) is equal to one, because each number has it's own identity, and you can't just keep going around saying that 1=2 or 2=3 because identities just can't change. saying 0.9999=1 is like saying you're 0.99 and 1 year old (wtf?) and that will simply complicate our already complicated math >:P
this is my own opinion, but im a math genius in class, and solving these kinds of problem is my expertise, and if you think my explanation is not possible, please explain to me why, no hard feelings ok.
there are strange math rules out there. For example, 1+1+0
(the * means square root of)
1+1 =
1+(*1)=
1+(*1x1)=
1+(*-1x-1)=
1+(*-1)(*-1)=
1+(*-1)2= <<<the two is a "squared" sign
1+(-1)=
1-1=
0
The proof is flawed. The flaw starts at the second step. Square root of 1 is not always equal to 1. Square root of 1 is equal to the absolute value of 1.
There is another mistake further along your proof at step four. Square root of -1 is not equal to square root of 1.
In order for a number to be different from another, you must be able to place another number between them. As you can not place a number between 1 and 0.999... they are the same.
It is simple calculus. If you take the integral of the equation (.999) (repeating)x and cut it up into infinitesimal pieces and then add those pieces up again taking the integral of .999(repeating)x you get 1.
also if you take the limit as .999 is approaching 1, you can expect to get one itself, because after doing a limit comparison, you will find that both .9999... and 1 converge at 1. So you can say that .999... equals 1 (that is how the calculator does it)
I am surprised that no one mentioned calculus :\\ but then again the general population of AG members are like 14...
wow DDX, u r so clever (How can u say the general population of AG is 14?) U must be a sorcerer, lol.
Our brain limitation (or perhaps we don't know how to use it 100%), scientists says, even Einstein only using 15% of his brain, - it's like to measure tsunami with ruler (Morningstar game)
I believe in some ways we evolve into the next level, but devolve in some ways.
calculator is a machine, it reveals what human says to reveals, it doesn't calculate.
I was in my class, when my teacher ask a 3784 X 2563 =... and suddenly i answer his question before everyone touch the calculator (everyone stare at me), but i don't understand myself how can i count that fast.
It's amazing to read this forum, so many people interested in 1+1=2 or not equal to, "teacher why 1+1=2?" Thomas Alfa Edison[b], makes me remember of Edison, he was drop out from school because he can't answer this question, later on without him(his invention, his idea) we can't even ask a question (because we don't have lamp and telephone until now). Can u guys imagine if we stil using candle in frontlight and backlight of our car?
Why does 0.9999... = 1 ? This answer is adapted from an entry in the sci.math Frequently Asked Questions file, which is Copyright (c) 1994 Hans de Vreught (hdev@cp.tn.tudelft.nl).
The first thing to realize about the system of notation that we use (decimal notation) is that things like the number 357.9 really mean "3*100 + 5*10 + 7*1 + 9/10". So whenever you write a number in decimal notation and it has more than one digit, you're really implying a sum.
So in modern mathematics, the string of symbols 0.9999... = 1 is understood to mean "the infinite sum 9/10 + 9/100 + 9/1000 + ...". This in turn is shorthand for "the limit of the sequence of numbers
9/10, 9/10 + 9/100, 9/10 + 9/100 + 9/1000, ...."
One can show that this limit is 9/10 + 9/100 + 9/1000 ... using Analysis, and a proof really isn't all that hard (we all believe it intuitively anyway); a reference can be found in any of the Analysis texts referenced at the end of this message. Then all we have left to do is show that this sum really does equal 1:
Proof: 0.9999... = Sum 9/10^n (n=1 -> Infinity)
= lim sum 9/10^n (m -> Infinity) (n=1 -> m)
= lim .9(1-10^-(m+1))/(1-1/10) (m -> Infinity)
= lim .9(1-10^-(m+1))/(9/10) (m -> Infinity)
= .9/(9/10) = 1
Not formal enough? In that case you need to go back to the construction of the number system. After you have constructed the reals (Cauchy sequences are well suited for this case, see [Shapiro75]), you can indeed verify that the preceding proof correctly shows
lim_(m --> oo) 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.
Another informal argument is to notice that all periodic numbers such as 0.9999... = 9/9 = 1 are equal to the digits in the period divided by as many nines as there are in the period. Applying the same argument to 0.46464646... gives us = 46/99.
remember, the limit approaches a number but never reaches it.
Hmm... lim x^2 when x->2 = 4 I'm having a brain blockade from thinking about infinity but this example illustrates the values that limit takes. x never is equal to 2 but limes is still 4. And we all now that 2^2 is indeed 4.
No need to go into some fancy high math. This proof is done in high school along with geometrical progressions. Sum that goumas 13 is mentioning in that proof upstairs is in fact sum of elements of geometrical progression that is calculated with a simple formula: sum = b1*((1-q^n)/(1-q)) That sum is 9/10 + 9/ 100 +... b1 is first element, n is the number of elements(infinity in this case) and q is that numbers with which we multiply the previous element to get the next (1/10 in this case). Put b1 and q in the previous formula and you'll get 1. Of course it is obvious that q^n=0 when |q|<1.
a) This thread does not, for all the stretches of my imagination, contain any discussion relevant to World Politics, Religion or Philosophy. There's no dedicated "Math" forum either, so I'm moving this to the tavern.
b) I was going to lock this because it's a zombie thread...but since the rigorous discussion only really begins after it was revived, I'll let it be.
0.000...0001 is just 0 because there's an infinite amount of zeros before you get to the 1, same goes for 0.000...2. Your not dividing by a fraction but by 0, this causes the errors like 1 = 2. I've seen this many times before, it's nothing new and special
