Ok I’ll answer one more post that’s it. You are wrong, you do not understand maths, and you are being illogical. It’s really as easy as that and its not my fault you can’t grasp infinity of .9s so go away and think about why maths works and what you are suggesting wouldn’t and never ever study anything to do with maths, because if your logic here is any indication you will be utterly lost beyond trigonometry and particularly in calculus. That’s not meaning to be insulting that’s just criticism based on the fact that not everyone has a mind that understands maths or the concept of limits. You are one of them I’m afraid, don’t worry though I’m sure whatever you decide to do with your brain will not involve any maths at all.
If maths didn’t work for the reasons you suggest which are totally erroneous anyway no one would use it, simple as that.
I’m well aware that equals in maths means numerically equal, as it does in the statement .999…=1 because it just does (limit x----->infinity)
Didn’t you say earlier you said there was no such thing as fractions. Which is not true. There is no such thing as .33333333333333333333333333333333333333333333333 of something, but as x approaches infinity there is, it’s called a third or 1/3.
Xeno’s paradox has been proven to be a faulty thought experiment about 1,000,000 times the only problem is that to understand why you’d need to understand some calculus. But let’s just say that the relation between distance and time is not as Xeno thought. And that as a ball bounces it will eventually approach the floor and remain still and leave it at that. If you’re interested Google Xeno’s paradox and there are hundreds of examples that explain it how it is pretty much a solved problem in maths and has been for thousands of years, Archimedes for example was the first to solve it, using something approximating calculus or Taylor series. Also take a brief look at the logarithmic decay function (mostly used in radioactive decay) explains Xeno’s paradox is not a paradox at all just sloppy maths. Put it this way if it was true an amount of radioactive caesium would never decay to 0, nor would half lives be half.
Put simply time and motion is continuous not in the way described by Xeno but by that described by integration and differentiation, since those models work with stupendous accuracy and Xeno’s paradox doesn’t I would go with the maths of today.
It doesn’t true but it would if infinity was real. That is the point of the concept infinity. Infinity means something of which there is nothing larger, which means that .999…=1 because it is infinite. So one cannot exceed it. That is the infinity paradox of maths that is used to make all maths work. It’s also very logical too, it’s just some people don’t get the logic and some people do.
“Infinity means something of which there is nothing larger, which means that .999…=1 because it is infinite.”
I don’t get that logic.
to me infinity is something which has no finite quantity. you cannot say that infinity means nothing is larger, because then the largest “thing” in question can have a finite quantity aswell as being considered “infinite”.
i don’t think we need paradoxes and proofs to make math work, it works regardless of how we perceive infinity.
you say that infinity makes .999[bar] equal one, i say it makes it as close to 1 as possible.
This is your problem you just said the same thing as I did, but you don’t realise it.
If you add something to infinity it is still all there is.
I don’t think there’s a problem with maths, I think there’s a problem with you and maths and how you understand it. Sincerely.
Everything that is anything else is smaller by definition, because it’s a sub set of everything. I know I’ve said this already but hell I’ll give it till 00:00 my time, and if you haven’t grasped it I think I’ll just have to accept you never will. As I said before some people get concepts like this some people don’t, don’t make the mistake of thinking what you think is right by definition of you being you. That way lies idiocy. There comes a time particularly in maths and science where a resort to consensus and authority is all there is left, this is that point. You either accept that or abandon hope of ever understanding maths. If the concepts are above you it’s analogous to accepting that I can’t speak Chinese, and no matter how much I hear it I will not understand it without some means of analogy, like someone pointing at a dog and saying quang or whatever a dog is in Chinese. I’ve seen this argument a lot and some people really just can’t get it. I don’t know maybe their brains are just wired differently, maybe they have no maths genes? But it’s never been resolved by a series of brilliant mathematicians on the forums I visit going, OMFG Now wait a minute, I’ve wasted my career, this guy with a highs school level of education is onto something, all maths is wrong and it’s back to square 1! I don’t think it can because it’s just not wrong, it’s axiomatically correct and logical. That’s why these people use it. There’s not some conspiracy to hide the Numberwang code from you.
1 does equal 0.9[bar]. its just mathematical fact, no way around it.
numbers are only abstract concepts, and in the abstract, the infinite limit which approaches a certain final finite number, is equal to that number in every way. in fact, technically since every number is only such a limit of infinite sums, ALL numbers are [bar] decimals (or rather, an open set of summed infinitely-receeding fractions) to infinity.
every rational number can be expressed as function curve on a graph, a curve which exponentially meets the number at infinity. yes, saying i have 0.9999999… slices of an apple and add them together, is not the same thing as saying that i have 1 apple. but, numbers are abstract; and you cannot have a material infinity, its a contradiction. so naturally, since infinity only exists in the abstract world of numerical ideas, that is where it is equal to the finite number it meets at infinity.
Interestingly although 1 is the prime numberwang, .999… is not numberwang, however .999… lim x---->{infinity-1} is of course numberwang. Not a lot of people know that.
I think it’s all been said infinities don’t exist maths axioms do and they are correct by definition that’s what an axiom is. You can’t argue that the concept of 1 is illogical any more than you can that .999…=1. It’s pointless.
One does equal 3 minus 2… There is no way around it, except that where a number cannot be shown, fixed, and finite; there it is difficult to say what it equals…You cannot say what 1/3 of anything is…It is not the answer, but the question 1 divided by 3…Put that in decimal form, and mulitply it by three, and you know the answer: 3/3 which is one… Keeping it in decimal form only reproduces the nonsense endlessly…It does not inform, and it does not illustrate, and it does not ease which is the purpose of all forms… We do not have forms like math because they muddy reality beyond comprehension, but because the give us knowledge… .999… is garbage for hogs…
Still campaigning this thread, eh? It’s got to be one of the ILP classics by now.
How 'bout this idea: we can define an infinitesimal as follows:
infinitesimal = x - y_max where x > y. That is, an infinitesimal is the difference between x and the maximum possible value for y when x > y.
That definition works for me, but I’m still a bit skeptical whether it is subject to arithmetic in the same way as all other numbers.
I seem to recall from my courses in calculus the difference between an open limit and a closed one. I forget which is which but one is a limit that can be attained whereas the other is one that can’t. So in the equation x^2 = y, for example, the limit of y as x approaches 2 (say) is 4, and it is an attainable limit (open/closed - I forget which) because x can equal 2. On the other hand, the limit of y as x approaches infinity is likewise infinity, and it is an unattainable limit because x can never reach infinity.
So the question that lies before us is this: in the equation sum(9/10^x) = y, is the limit of y as x approaches infinity an open or closed limit? In either case, the limit of y is 1. But is it an attainable limit?
You seem to argue that y_lim is unattaible, which tells us that y_lim as x approaches infinity - 1 = infinitesimal, but I say y_lim is attainable, which tells us that y_lim as x approaches infinity - 1 = 0 and so y = 1 as x approaches infinity.
Who’s right?
Well, I would say that I’m not sure, but the proof given in the OP seems to settle the matter for me - the limit is attainable.
you think infinities are grabage and do not give knowledge? tell that to all of calculus, which, given its history of leading to the mathematical knowledge-base for scientific theories spanning all of physics (along with all of the real-world material technology these theories have generated) and beyond, might beg to differ.
symbolic representations of infinities or unending sums/sets are indeed very practically useful.
fractions (i.e. percentages or relations) are no different fundamentally than decimal numbers. they are symbolic-language ideas meant to represent a QUANTITY of/and/or relative value. you can indeed have a quantity of 1/3 of X, and this DOES indeed give us added meaning: we learn that the total quantity of X is 1/3, or 33% of its maximum (full) possible value.
fractions represent ideas of probability as well as quantity; these are two distinct aspects where we are given knowledge by these symbolic representations… and by this measure, you might even consider a fraction (i.e. think of it also as a RELATION between TWO numbers) as providing more information than a single number by itself… 1/3 gives more information that 1 or 3, because the concepts of the quantities 1 and 3 are both contained within 1/3.
Almost our entire social reality is made up of infinites that are alternately useful and useless… God is as much an infinite as justice or liberty which are moral concepts, which is to say: spiritual forms… I think it would be great if we only had finites to deal with, but then, we would not be human, and certainly not what we are… So if you find mathamatical infinites useful; then by all means, enjoy them…It does not matter to me, but it should matter to you when the basic identity behind all math, that one is one should be supplanted by an infinite representation of one which is hardly useful, and so, is pointless… Ultimately, all our concepts are not useful because they are truthful, but are tuthful because they are useful… I would ask what use has the representation of one as .999…??? If it has no use it has no truth… No matter with what form we represent reality, it must ease our lives to tell us truth…The truth as we have it, that life is difficult, and complicated is not the one we desire… We want a new truth… .999… is just reinventing the wheel out of a log…It does not us get closer to a desired reality…
Juggernaut, if you ever take advanced math or physics or any hard science you’ll see that, far from useless, infinite decimals like 0.9[bar], and identities like 0.9[bar] = 1, are essential for analyzing all sorts of practical problems. They help us make predictions about the world. Without them, many concepts in math would cease to exist, and the applications of those concepts in the sciences would become impossible. You owe the computer you’re typing this on to a human mind that designed it, and that mind used infinite decimals and infinite series identities to design it. So in a way, you owe the computer you’re typing on to 0.9[bar] = 1. What could be more useful or real than that?
Now wait a minute, I’ve wasted my career, this guy with a highs school level of education is onto something, all maths is wrong and it’s back to square 1! I don’t think it can because it’s just not wrong, it’s axiomatically correct and logical. That’s why these people use it. There’s not some conspiracy to hide the Numberwang code from you.
