ROFL !
Me thinks this place is driving you a little bananas sir
i see ur point though, lerts you did just walk in mumbling about how great you are
ROFL !
Me thinks this place is driving you a little bananas sir
i see ur point though, lerts you did just walk in mumbling about how great you are
great results i see there. did you notice that it says 'extended' real line? as in, "stuff you can do, theoreticaly, about quantities that can not be measured" ? you can add stuff up. countable stuff. you can't count to infinity. you can't do arithmetic with infinity. and by 'arithmetic' we mean "add quantities up and come up with real results".
0.333... is not an approximation. it is the decimal form of 1/3. quit insisting. it is an other way to write 1/3. it is not just equal.
here you go about arithmetic: http://en.wikipedia.org/wiki/Arithmetic see any mention of infinity? also note that it says "These new elements (+/-inf) are not real numbers"
an entire page on wikipedia, devoted exactly on this subject, with proofs, references and whatever, by knowledgeable people, doesn't just give you the idea that you just might not have understood something?
you sound like lerts trying to "disprove" the conservation of momentum.
Are you sure, that would imply negative infiinity equals 0.
I think it is possible to measure infinity in quantifyable terms in a slightly different way to normal mathematics. Some people have mentioned how they visualise a quantity of something, well, one way to grasp negative infinity might be to measure the negative vibes coming off a particularly emo goth chick. You could do the same with infinity by measuring the hotness of Milla Jovovich (the 5th element).
I think these quantify the concept of infinity very well, and think i'll adapt all my mathematical calculations to a similar scale based upon shaggability.
sorry but what?
Sorry for my ignorance
Anyone care to explain what this is?
It's math's
i thought the romans had no concept of zero? (may have them mistaken with some other ancient culture)
one of the many reasons why they didnt invent financial math and balance sheets and their only contribution to modern life is the diameter of the shuttles boosters
why limit the extension to the needlessly mundane ¥?
of course you can... otherwise how would you explain the difference between countably infinite and uncountably infinte?
Errrrr.
1/3 (as in the fraction 1 over 3) = 0.3333333... (recurring - with me so far?)
1/3 x 3 = 1 (obviously - three thirds of something will always equal 1 - slice a cake in 3 ways, and keep all the slices. How much cake is left? All of it)
0.3333333... x 3 = 0.99999.... (recurring)
However if 0.333333... = 1/3, then surely 0.9999.... = 1?
At the same time, 0.33333 x 30 = 9.99999.....
9.999999 - ( 3 x 0.33333) = 9
EDIT - Bad idea explaining stuff when tired.
No they don't, if you are clear on what the representation means: e.g. 0.12 is a shorthand notation for 1*10^-1 + 2*10^-2. This is how decimal notation is defined. 0.9~ means an infinite sum of 9*10^-n where n goes from 1 to infinity. This sum converges and is a well defined number: exactly 1.
It's amusing that you dismiss a mathematically correct proof that 0.9~ is 1 (the one with 10*x-x=9), because you say it uses infinities (which it doesn't, btw) and here you make an argument of your own using an arithmetic with an infinity.
Think about the following mistake as well:
0.9, 0.99, 0.999, 0.9999, ... this tends to 1.
0.9~ is a representation of a single number and it doesn't tend to anything. To have a notion of tending, you need to have a sequence.
No. I also think that 0 is not nothing. That's why I said that 1/infinity=0. But zero isn't nothing IMO, it is just an infinitely small value. 1/something is it's reciprocal. If infinity is infinitely large, then it's reciprocal must be infinitely small, yes? I was just using 0 to represent an infinitely small value, which I believe it does.
So, I think that: 0.999... + 0 = 1, and 1 - 0 = 0.999...
That's my theory. But, I do NOT think that 0.999... equals 1. It can be represented by the number 1, though. Perhaps 1 means 0.999... although they are not equal. We just use 1 to represent 0.999... Maybe there is no such thing as a real number. Any number that has an end to it is actually that number minus an infinitely small value in my opinion. So 3 represents 2.999... and 0.92 represents 0.91999...
That is my theory. I don't think that it is incorrect, or correct. It's just how I perceive it.
0.9~ tends towards 1 because it is an infinitley increasing number and hence DOES tend towards 1. It is IMPOSSIBLE to represent a single value because it is infinite in size.
infinity - 1 = infinity and therefore infinity is NOT a single number but an abstract concept for values that are impossible to represent.
If the concept of 0.9~ is a valid number you MUST accept that 0.1*10^(-infinity) is also a valid number.
Given this then the following is valid because 0.9~ is always 0.1*10^(-infinity) away from 1, it is impossible for it to be anything else.
1 - 0.1*10^(-infinity) = 0.9~
This means we have established a VALID way to create 0.9~ that involves subtracting a value from 1. this means...
0.9~ < 1
And therefore
0.9~ != 1
So which part of the above is NOT true. Please do not just spout the "what you learnt in school as a kid and have taken as gospel" that 1/3 = 0.3~. Why is the following NOT valid
1 = (3 * 0.3~) + 0.1*10^(-infinity)
infinity - 1 = infinity and therefore infinity is NOT a single number but an abstract concept for values that are impossible to represent.
If the concept of 0.9~ is a valid number you MUST accept that 0.1*10^(-infinity) is also a valid number.
Given this then the following is valid because 0.9~ is always 0.1*10^(-infinity) away from 1, it is impossible for it to be anything else.
1 - 0.1*10^(-infinity) = 0.9~
This means we have established a VALID way to create 0.9~ that involves subtracting a value from 1. this means...
0.9~ < 1
And therefore
0.9~ != 1
So which part of the above is NOT true. Please do not just spout the "what you learnt in school as a kid and have taken as gospel" that 1/3 = 0.3~. Why is the following NOT valid
1 = (3 * 0.3~) + 0.1*10^(-infinity)
Since people are taking this thread seriously...
If you didn't play LFS today (read: you played LFS zero times today), how many times did you play LFS today? hint: it is not an infinitely small value, unless you sleepwalk or something...
@0.999... discussion: 0.999... does not tend to anything, it's just 0.999... What tends to 1 is it's estimate value, wich we created to make real life applications possible (you can't do math with a number when you don't know it's exact value - like 0.999...).
If you didn't play LFS today (read: you played LFS zero times today), how many times did you play LFS today? hint: it is not an infinitely small value, unless you sleepwalk or something...
@0.999... discussion: 0.999... does not tend to anything, it's just 0.999... What tends to 1 is it's estimate value, wich we created to make real life applications possible (you can't do math with a number when you don't know it's exact value - like 0.999...).
I'm not saying that 0.999...=1, I am saying that 1 does not exist, but that we use 1 to represent 0.999... because we are just rounding up.
The effect on the train could be termed "chassis flex"
If 0.9~ tends towards 1, then I would like you to write out formally what sequence are you talking about here, i.e. what is a_1, a_2 etc. so that a_n tends to 1. Only sequences tend towards something.
And, btw, infinitely increasing number - this phrase in this context makes no sense. Any real number has a particular value, it cannot have an increasing value. 0.9~ is a representation of a SINGLE number. This reminds me of "1+1 is equal to 3 for very high values of 1".
I know what you're getting wrong and already wrote about it: you keep thinking of 0.9~ as a number for which you add more and more decimals. This is not correct: 0.9~ is the number you get *after* you add everything.
This doesn't follow: 0.9~ is a valid decimal representation - there can only be powers of 10^-n for integer n, no 10^(-infinity) coefficients, so it's not a valid number written in a decimal representation. Look up decimal representation.
And even if you wanted to extend it this way, then you MUST define this as 0. If it's a number, then it has a definite value. What you would like it to be: "A number bigger than 0 and smaller than any other number" is NOT a valid number.
Yes, 0 away
0.3~ is a precise thing in math - a sum of an infinite series. And it is equal to 1/3. 0.1*10^(-infinity) is your concoction with some purported properties that go against the axioms of real numbers.
Errrrrumm... just give us a dollar.
The problem with maths is it never accounts for the bit you need to lick off the knife.
If you cut a cake there's ALWAYS some left on the knife, thats the missing .0001 so that accounts for the .3333 if you cut a cake in thirds.
There's always a bit left on the blade so you can never reach more than.9999999999 recuring due to my stunning theory explaining the knife effect.
Maths is simple really .....................
Math people have perfect knives.
So infinite is equal to zero then?
So if you cut the cake into exact thirds of the original cake, there is cake on the knife?
Congratulations on making Cake magically appear.
Actually that if the BEST way to explain the fact that 1/x where x=numberBase-1 - 0.1~
Come on people, face it... Any 0.x~ is a bodge where the number is not easy to represent in the base you are trying to represent it. You can wrap the notion up how you like, say the limit of 0.9~ is 1 or whatever else you like but is a bodge imposed by base 10.
As I said before. 1/3 in base3 is 0.1 as nice clean number that does not need a bodge. move to another base and BANG... bodge time
1/3*3=1 fine but when you try and represent in a given base things turn to shite and you need bodges liKe 0.3~ * 3 = 0.9~ = 1
Is this a very well disguised troll attempt?
But the whole point Woz is that it ISN'T a bodge, a flaw or an inaccuracy. Rather it's your understanding of the concept of numbers and infinity that needs updating.
That 0.999... = 1 is not particularly advanced mathematics.
That 0.999... = 1 is not particularly advanced mathematics.
No, I have been around this forum for YEARS. If I wanted to troll I would have many times before. This is in OT is it not?
I started out wanting an answer and have yet to get one. All I get is the 10x-x "proof" and people saying that 0.9~ because it is ok!.
Even the Wikipedia post on 0.9~ has the follow phrase contained...
"Misinterpreting the meaning of the use of the "…" (ellipsis) in 0.999… accounts for some of the misunderstanding about its equality to 1. The use here is different from the usage in language or in 0.99…9, in which the ellipsis specifies that some finite portion is left unstated or otherwise omitted. When used to specify a recurring decimal, "…" means that some infinite portion is left unstated, which can only be interpreted as a number by using the mathematical concept of limits."
Let me repeat that VITAL part... "When used to specify a recurring decimal, "…" means that some infinite portion is left unstated, which can only be interpreted as a number by using the mathematical concept of limits."
That unstated part being my disputed 0.1*10^(-infinity) or the knifes share or the sliced cake
When you get into limit theory you accept that while 0.9~ never actually converges with 1 you accept it is 1. Again, you accept that it is really impossible to represent 1/n when n=base-1 yet there is a need to find a way to solve this problem
so 1/3*3=1 yet 1/3 can't be represented by base 10 without a bodge, yet nobody is willing to accept this yet is more than happy to break every rule in the base 10 number system to create a solution to the problem.
Why?
Where is the best place to read up on this then that does not fall back on 10x-x as the only proof?
"There are many proofs that 0.999… = 1, of varying degrees of mathematical rigour. A short sketch of one rigorous proof can be simply stated as follows. Consider that two real numbers are identical if and only if their difference is equal to zero. Most people would agree that the difference between 0.999… and 1, if it exists at all, must be very small. (WOZ: but as it exists it must be able to represent.. hence bodge) By considering the convergence of the sequence above, we can show that the magnitude of this difference must be smaller than any positive quantity (WOZ: Why?), and it can be shown (see Archimedean property for details) that the only real number with this property is 0. Since the difference is 0 it follows that the numbers 1 and 0.999… are identical. The same argument also explains why 0.333… = 1⁄3, 0.111… = 1⁄9, etc."
So that has not shown it then. Just saying the difference is so close to zero we will call it zero is not proof
well, on the Wiki page there are 62 notes and a similar number of references, plus a few external links. Failing that there are always libraries or teachers. Perhaps visit your local university's mathematics department?
A good quote from it, which might help you understand, "there are no nonzero infinitesimals". i.e. with an infinite number of 9s after the decimal point there is no 'small portion' not accounted for.
A good quote from it, which might help you understand, "there are no nonzero infinitesimals". i.e. with an infinite number of 9s after the decimal point there is no 'small portion' not accounted for.
0.9999..... = 1
(166 posts, started )
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