Current mood:

frustrated

How people argue online
Before we start, I would like to point out that 0.9999... with an infinite number of 9s is equal to 1:

0.3333.... an infinite number of times is exactly one third.
0.6666.... an infinite number of times is exactly two thirds.
0.9999.... an infinite number of times is exactly three thirds. But three thirds is equal to one.

With me so far? Good.

Someone wrote about this in the Guardian, saying his daughter's maths teacher had explained this to him. The comments section is worth reading if you want an understanding of the way people argue about things they don't really understand, especially online.

Several people build straw men. One attempts to prove to us all that 0 followed by a finite number of 9s is not equal to 1:

How about trying your number games with money. 0.9 pounds (90p) is equal to x. y is equal to 1 pound. Think of a number greater than x but less than y. Easy, 99p. i.e. 0.99 pounds. Even better, 0.9 million pounds. is it equal to 1 million pounds? if you think so, then I will gladly write you a cheque for 0.9 million pounds in exchange for your cheque drawn up to the sum of 1 million pounds.

One person appears not to realise that (y-x) can equal zero in

"Can you think of a number that is higher than x but less than y? No, you can't." Yes, I can. x + (y-x). Teachers eh?

Another person attempts a stumbling explanation of why he believes that the numbers are different, and ends up by explaining:

All a bit of bollocks really - as usual, when you get what looks like a paradox, it's because your starting conditions are incorrect - in this case it's because infinitely recurring numbers don't actually exist. (my emphasis)

Yes, folks, you've never divided anything into thirds, because the number one-third doesn't actually exist. And then there's someone who writes in support of that comment using the age-old argument of questioning the sexuality of anyone who disagrees with him:

I for one will take [this user]'s common sense mathematics over any amount of pointy headed claptrap from some four-eyes who’s probably working on a thesis about “lesbian algebra” (grant aided no doubt).

(76 comments) - (Post a new comment)

	naath 2006-06-22 01:21 pm UTC (link)
	People are SO STUPID! (Reply to this) (Thread)

	(Anonymous) 2006-07-17 10:37 pm UTC (link)
	We are all people, aren't we? (Reply to this) (Parent)(Thread)(Expand)

(no subject) - litch, 2009-07-15 04:38 am UTC (Expand)

	jaq 2006-06-22 01:23 pm UTC (link)
	I think it's good to be reminded occasionally that some things I find obvious are not understood by some people. (Reply to this)

	chrissmari 2006-06-22 02:03 pm UTC (link)
	I never learned that .9bar was equal to 1 it makes sense with your explanation and i learned that about .3bar and .6bar haha weird lj teaching you something knew everyday (Reply to this) (Thread)

	chrissmari 2006-06-22 02:09 pm UTC (link)
	knew was not a purposeful typo though it would have been clever if it was (Reply to this) (Parent)

	senji 2006-06-22 02:09 pm UTC (link)
	Argh, it's all so wrongheaded. Even the original article. (Reply to this)

hitchhiker 2006-06-22 02:26 pm UTC (link)

I tried to explain that a sequence of ten heads did *not* mean that "tails was now more likely to come up since it had to average out to .5" to a (very intelligent!) English major. She wasn't convinced. Apparently, "probability is still a not-very-well-understood branch of mathematics", to which I tried to explain the distinction between pure mathematical combinatorial probability and statistical probability, but she wasn't buying it. Also, she believes in "intelligent guidance", since the mathematics of the situation don't allow enough time for pure evolution to have evolved life of the diversity and complexity we see today. Sigh. (Reply to this) (Thread)

onib 2006-06-22 02:45 pm UTC (link)

Most people never seem to quite grasp probability. My mother suffers from a genetic condition which is passed on through a dominant allele. Her doctors explained that her children would thus have a 1-in-2 chance of inheriting the condition. When my brother turned out not to have it, she spent the next several years convinced that I must have it no matter how many tests proved otherwise because...wait for it...she had two children, and she knew one out of two would develop it. I still can't explain probability to her. (Reply to this) (Parent)(Thread)(Expand)

(no subject) - marnanel, 2006-06-22 02:47 pm UTC (Expand)

(no subject) - onib, 2006-06-22 02:49 pm UTC (Expand)

(no subject) - secretlondon, 2006-06-22 08:03 pm UTC (Expand)

(no subject) - marnanel, 2006-06-22 02:50 pm UTC (Expand)

	onib 2006-06-22 02:38 pm UTC (link)
	That's really astounding to read. I'm shocked, and yet not shocked at the same time. Wikipedia Schmickipedia, I’m sorry but I simply don’t approve of any of this “fannying about” with our British numbers. Now, you own the numbers, too?!? Wow! (Reply to this) (Thread)(Expand)

	marnanel 2006-06-22 02:40 pm UTC (link)
	Sure, we invented decimal arithmetic. Either that or we invaded the people who did at some point, which is almost as good. Or something. :) (Reply to this) (Parent)(Thread)(Expand)

(no subject) - onib, 2006-06-22 02:47 pm UTC (Expand)

(no subject) - phyphor, 2006-06-22 03:08 pm UTC (Expand)

(no subject) - firinel, 2006-06-22 03:20 pm UTC (Expand)

(no subject) - torquemada, 2006-06-22 03:59 pm UTC (Expand)

(no subject) - onib, 2006-06-22 03:29 pm UTC (Expand)

(no subject) - haggis, 2006-06-22 07:43 pm UTC (Expand)

	chani3 2006-06-22 02:54 pm UTC (link)
	mmm. math. I never understand how to talk to people that have a fundamental inability to use logic. (Reply to this)

	queenmomcat 2006-06-22 02:58 pm UTC (link)
	Zeno's arrow much? (or Xeno. I'm not sure which.) (Reply to this)

	(Anonymous) 2006-06-22 03:05 pm UTC (link)
	It's really not that hard to prove otherwise, either: x = 0.99999... 10x = 9.9999... 9x = 9 x = 1 (Reply to this) (Thread)

	wrong (Anonymous) 2006-06-23 05:18 am UTC (link)
	If x = 0.99999... then 9x = 9 * 0.99999... = 8.99999... Check it out for your self. (Reply to this) (Parent)(Thread)(Expand)

Re: wrong - phlebas, 2006-06-23 01:04 pm UTC (Expand)

Re: wrong - (Anonymous), 2006-06-23 04:15 pm UTC (Expand)

Re: wrong - phlebas, 2006-06-23 04:24 pm UTC (Expand)

Re: wrong - (Anonymous), 2006-06-23 10:37 pm UTC (Expand)

It's funny (Anonymous) 2006-06-22 03:09 pm UTC (link)

I agree with the fact that 0.99...=1. However, it occurs strange to me that there is only countably infinite amount of digits in a presentation which should match with a element from a set which has uncountably infinite number of elements. It obviously follows that only rational numbers can be expressed with infinite recurrences and, on the other hand, irrational numbers (uncountable set) cannot be. Right? (Reply to this) (Thread)

	Re: It's funny marnanel 2006-06-22 03:16 pm UTC (link)
	Right. The decimal expansion of irrational numbers doesn't repeat (well, it doesn't repeat in any base). (Reply to this) (Parent)

	cdk 2006-06-22 03:20 pm UTC (link)
	That's just a very painful read. I respect that some people simply don't "get" math, for whatever reason, but it's always frustrating to watch them try to ensure that no one else gets it, either. (Reply to this)

rethought 2006-06-22 03:26 pm UTC (link)

I took maths up to Intermediate Calculus. And then I gave up. (Mostly because, while I understood what I was doing, it took me hours to get there for a single problem.) There are some basic maths ideas that I still get aggravated trying to wrap my head around. Like multiplying negatives. 'Two negatives, when multiplied, will produce a positive result'. Huh? I dutifully performed this function for years, secretly rolling my eyes and thinking (in a sing-song voice) this isn't possible! I'm sure that if I spent a good amount of time trying to figure it out, I would. I'm sure if I spent a good amount of time trying to figure out American Football, I would get that as well. But, I'm not going to. Why? Because I'm okay with believing the mathmaticians. Some people take God on faith alone with no understanding...I take negative integers on faith alone. And, you know, my time is better spent honing my language skills on the main, and using the maths skills I do have on occasion than beating my head against a wall about -2 x -2 = 4. Does this mean I never question anything in maths? Hardly. Does this mean that I'm a poor mathmatician? Hell, yes. Just saying. (Reply to this) (Thread)(Expand)

(Anonymous) 2006-06-22 04:24 pm UTC (link)

Well, at least you just believe those that (seem to) know more than you do... Many people are way to stupid to understand even basic mathematics, yet they stubbornly believe the biggest nonsense, in spite of mathmaticians telling them its wrong. Same situation with economics, really. Many people just don't get it. But still they have very strong opinions about it... And of course, check all those believing in aliens and stuff... Or in alternative medicine. Not that there are no working alternative medicines, but it's rather stupid to believe they DO work, while you think the hospitals sell you expensive, non-working stuff. (Reply to this) (Parent)

(no subject) - phyphor, 2006-06-22 04:39 pm UTC (Expand)

(no subject) - rethought, 2006-06-22 05:16 pm UTC (Expand)

(no subject) - (Anonymous), 2006-06-22 11:15 pm UTC (Expand)

(no subject) - rethought, 2006-06-22 11:54 pm UTC (Expand)

	Nope. (Anonymous) 2006-06-22 03:34 pm UTC (link)
	Sorry, can't agree that 0.9999.... an infinite number of times is exactly three thirds. Mathematically speaking, the limit of 0.999... for number of digits of nines approaching infinity is 1. :) Jan (sorry 'bout poor english) (Reply to this) (Thread)

Re: Nope. diskgrinder.myopenid.com 2006-06-22 04:16 pm UTC (link)

No, wrong. Except you have a kernel of half truth almost there - yes, any finite sequence of 9's after a decimal point approaches 1 as you add another 9 on the end (see, it's a process), but we're not talking about a process - the number .9bar is not a process, it's another name for 1, a mark on the number line, not a moving target, continually getting closer to 1. (Yes, the number 0.999 is closer to one than 0.99, but 0.999 and 0.99 are different numbers: each time you add a 9 you get a new number closer to 1). Put another way, when you talk about 0.99, 0.999, 0.9999 etc. approaching 1 you are talking about a sequence of numbers, not the number 0.9bar. (Reply to this) (Parent)(Thread)(Expand)

Re: Nope. - bogado, 2006-12-19 03:50 pm UTC (Expand)

decimal numbers (Anonymous) 2006-06-22 03:36 pm UTC (link)

0.3333... is the decimal representation of one third (1/3) 0.6666... is the decimal representation of two third (2/3) 1 is the decimal representation of three third (3/3) and it's equal 0.9999... unless you need a number less than one. You can't differentiate abs(x-1) at x=1. When differentiating you need to leave the 1 out. "x≠1" which is equal to "(x<1 or x>1)". If you think of the number highest number less than 1 (and thus as much near 1 as possible) you may think of 0.9999... because you can't tell me the difference between 0.9999... and 1 but you know there is one. => x ∈ R\1 The best way is to use fractions in general and avoid repetetive numbers. (Reply to this)

	xlerb 2006-06-22 05:47 pm UTC (link)
	I think I'll view 0.99999… as the fixpoint of f(x) = (x+9)/10; that is, the value of x such that f(x)=x. This is also, due to the contraction mapping theorem, the limit as n approaches infinity of passing any number through f n times. So, x = (x+9)/10; 10x = x+9; 9x = 9; x = 1. (Reply to this) (Thread)

	Wrong (Anonymous) 2006-06-23 05:35 am UTC (link)
	f(x)=(x+9)/10 does not equal 0.9999... First of all 9/10=0.9 which doesn't come close to ifinity. And adding x to the 9 before dividing by 10 again doesn't give a number that will approach infinity. 0.9999... will get infinitly closer to 1 but never will equal one. It can only equal 1 if at some point it is rounded up. (Reply to this) (Parent)(Thread)(Expand)

correct. Re: Wrong - (Anonymous), 2006-06-23 04:24 pm UTC (Expand)

(Anonymous) 2006-06-22 06:36 pm UTC (link)

I've asked myself, "How can I understand this situation?" I've put my answer in the form of answers to several subquestions: What can I know about the question itself? What can we say about the argumentative form? Who knows the answer? What would a good answer look like? Let's look at the question itself, first: "What can I know about the question itself?" We know that: The question is of limited utility. (That is, there is little practical value, to most people, responding to the question.) The question is easy to form an answer to. (Leading to bike-shedding. (http://www.bikeshed.org/)) Third, the question is interesting. The existence of this argument itself can be taken as supporting evidence for the idea that regular people have at least some interest in mathematics. Finally, and perhaps most interestingly for our purposes of understanding the argument we see here: The question spawns further questions. If we say ".99999-", going on forever, what exactly does that mean? Is it a process? Or is it a value? Just what kind of number is .999999-? What kind of number is a number with a bar over its head? Just what kinds of numbers are there? How do we classify them? Just when do we say that they are equivalent to one another? (Programmers may classify 2+2 as an expression, and 4 as a constant. Mathematicians may have multiple languages for classifying these sorts of things, and have different ideas about their classification, though they would agree with each others conclusions, provided they took the time to learn the others' language. It's conceivable that by some sets and operations, .99999- is different than 1, and by just applying a different operator, perhaps "equal-sign mark 2," they are equal.) Another question: When people say ".9999- is equivalent to 1," what is the mathematical dialect that they are speaking in? That is, what is the authoritative mathematical foundation that most people use in their day to day mathematical reasoning? This may surprise some people here, but there are multiple schools of mathematical thought. They are unified in their acceptance of logic, but even there, there is some trouble: mathematicians seriously debate over what representation of logic should be "foundational," and which should be "derivative." People choose different starting points for these sorts of things. So back to our discussion: What is the name of the group or foundation or book or system of mathematics, that is foundational to our convention discussions, in which ".9999- is equivalent to 1" is authoritatively true? And the greater point here is that the question "Is .9999- equivalent to one" -- spawns off numerous questions. It is by no means the only question we are asking here; It is merely the focal point of questioning. And again: The initial question that this comment is answering, is: "What's the situation here?" I'm trying to observe, from overhead, what I see happening in this forum. Next, what can we say about the argument itself? How are people arguing here, and at broad? We saw a list at the beginning of the initial post: "Straw Men," was one item. We saw contempt for common people: "All bollocks, really..," not to mention marnanel's post itself. We saw Libertarianism rear it's ugly head: "Lesbian algebra, with grant aid no doubt," a contender on just about any discussion on any topic. (Libertarianism, clearly, refuses to be contained to any boundaries; Perhaps we should call this "Libertarian algebra.") We see numerous weak arguments, for and against. (continued) (Reply to this)

(Anonymous) 2006-06-22 06:37 pm UTC (link)

In short, this is really no different than the sort of everyday problem solving that we all apply, day to day. As Einstein said, (and I'm paraphrasing,) "It's not that I solve problems differently; it's just that I stick with my questions for longer." Einstein also applied the same sort of shoddy problem solving techniques that we all do. If we all, as a forum, asked and poked and prodded using the exact same techniques we used here; As long as we earnestly continued to try to solve the problem, we would eventually come up with satisfactory answers. It happens that there's an institutional form of doing just exactly this; It's called "becoming a mathematician," and they just sit around all day doing exactly what I described, and doing exactly what the people in these forums are all doing. Problem solving is experimentation, problem solving is hardly "logical," it comes from multiple angles (even the Libertarian angle,) and involves jumbles of motivation (you're answering the question itself, in the first place, after all,) and reason and the irrational, all together. What we see here is nothing to be ashamed of, in my book, (and I am deviating from the question: "What do we see at work here," to make this side comment-) We are seeing the hallmarks of what is known more widely as: "Defeasible Reasoning," (http://william-king.www.drexel.edu/top/prin/txt/Intro/Eco112c.html) something I highly recommend learning about, for people who are interested in just this sort of situation. If I may moralize again, for a moment: We should be cautious, when we try to explain these sorts of situations. We should struggle to see the brain at work here. We should be cautious, before we vent frustration with humanity. We should be cautious, before we vent anger at the "stupidity" of others. Because: We're often times just as guilty as the others, more often than not. If you doubt this, I invite serious self-observation and introspection. Back to explaining what we see here, in the argumentative form: Nowhere, interestingly enough, do we see an actual, convincing, explanation. We see numerous arguments for one interpretation, or for another, but nowhere, do we see an actual, convincing, explanation. (Perhaps it's just too expensive to provide..!) We see, almost universally, attempts to answer the question. Why is that? Perhaps the conversation was introduced in a confrontational way- "Are you with me? Good." Perhaps that was perceived as a threat, causing us to "take sides," or something. It may be that this is just a crowd that values appearing smart, and people are trying to do that. It may be that this is sort of like naturalistic explanations for religions: We see something we don't understand, and it opens up this profound hole in our being, and we must try to explain it away, as quickly as possible, and then with as much force of conviction as possible. Or perhaps people are earnestly trying to solve this problem, and throwing in their two cents towards its resolution. Or some combination of all of the above, and a bunch of things I don't even know. This interaction is very complicated; I don't know why we are doing what we do here; It would be really neat if I did. (continued) (Reply to this)

(Anonymous) 2006-06-22 06:38 pm UTC (link)

One common theme here, that I observe here, is the struggle between what I'll call: "My Library Science is Greater than Yours," vs. "I'm going to Think For Myself." The library scientists here (hang with me for a moment) are the people who don't know the answer themselves-- rather, they know who to trust, and who to talk with, to get the definitive answer. In many respects, this is called "being smart." It can even be modelled as a conservative thrust: Conservative to the established scientific-technological complex, or something, if we want to frame it in controversial terms. And it happens that mathematicians actually know what they're talking about, and that that trust is well earned. (So I believe.) I'm calling it "library science," because that's all about knowing where to turn, and what to trust, and so on. On the other end is: "I'll think for myself." "I won't be swayed, by flim-flam appeals to authority." "You're going to have to show me a real solid argument, that I can understand, and that I can believe." I think I can see these two expressions living underneath the surface of many comments around here. Who knows the answer? (to the base question: is .9999- the same as 1?) Let's rephrase that: Who understands the whole answer, and the whole question, to the satisfaction of derivative questions, and can persuasively explain it all to us? Clearly not the parents. Not marnanel either. And none of the commenters in here, either. I don't know the answer; I only hold further questions. (Innocent questions, I assure you.) Does the math teacher hold the answer? It doesn't look like it: This whole situation wouldn't have arisen, had the math teacher answered everyone's questions to satisfaction. That said, we do not know that the math teacher has been given the opportunity to do just that. We like to believe that knowledge exists perpetually, pristinelyt, floating above in the heavens, for all to either see ("intelligence,") or not see ("low IQ, stupidity," and so on.) In reality, knowledge is created through complex and time consuming processes, and must be communicated through complex channels (the make-up of which includes motivation and so on and so forth.) Very intelligent people will get things wrong all the time; It's simply essential (if we are to answer: "What's this situation about?") to recognize these things. Finally, what kind of answer would I like? What kind of answer do I think we could look at, and say, "Ah, there is the answer to this question." The answer would explain how to resolve numbers like ".9999-", 3/3, and even 1, for that matter. Perhaps we would understand 3/3 as a "rational," 1 as belonging to multiple systems (having an identity element is a requirement for every group, field, and ring, after all.) And what about that ".9999-" -- is that a real? Or is it merely an alternative encoding for a rational? What system of rules is at play here? The answer would explain how 3/3, 1, and .9999- are different, and how they are the same. Again, clearly, at least notationally, they are radically different; Just as "2+2" is clearly radically different than "4." The answer would shed light on the relationship between limits, and "static" numberes. We would understand the whole "process" vs. "value" thing. We would understand ".9999-" in this light. Is an sequence of digits with a bar overhead taken to be equal to the limit of that sequence? If so, why? What did mathematics benefit, by doing things that way? What questions were they resolving, when they decided to do that? Is there some notation for a thing that is not 1, that does represent the process of getting closer and closer to 1, but not ever actually reaching it? Can we construct a line, for example, that is missing the point 1, but that has every single little point leading up to it, and not getting there? (I happen to know that the answer to this is: YES!) The answer would explain how these concepts are rooted in present day mathematical thinking. What mathematical systems we're using, how it was determined in schools that we use this system, and so on. (continued) (Reply to this)

(Anonymous) 2006-06-22 06:39 pm UTC (link)

So, in summary: Our situation is of an interesting, multifaceted question, that's of limited utiltiy, and easy to make up answers to. We have a bunch of defeasible reasoning going on, and a bunch of people who are cock-sure they have the answer, even though nobody's answering the question. And if we mine our collective answers together to find the questions that underlie them, we can actually formulate a total question that gives us some greater insight into what is actually at work here. (Reply to this)

haggis 2006-06-22 07:26 pm UTC (link)

My response to this sort of thing shows why I'm an engineer. My first thought is "0.999999 recurring is as near to 1 as to be effectively 1, anyway." My second thought "To what accuracy do I need to know this anyway? If I'm measuring parts per million (eg for contaminants in water) it might make a difference." My third thought "Oh, this is infinite. So the further along the series I look, the closer to 1 it gets." So yes, to engineering accuracy, 0.9 recurring = 1. To be honest, I would have thought 0.9 recurring was always less than one but by such a tiny margin that it is effectively 1. (Reply to this) (Thread)

marnanel 2006-06-22 07:35 pm UTC (link)

To be honest, I would have thought 0.9 recurring was always less than one but by such a tiny margin that it is effectively 1. I think a mathematician would agree with you, but point out that the "tiny margin" is in fact zero, and thus the two numbers are the same. I'm sure a real mathematician like gjm11 or phlebas will be along in a bit. (If you say that 0.999... is 1 minus an infinitisimally small but not zero amount, you're effectively saying that 0.999... is the "next" real number below 1. But that's clearly silly, since there are uncountably many real numbers.) (Reply to this) (Parent)(Thread)(Expand)

(no subject) - (Anonymous), 2006-06-22 07:43 pm UTC (Expand)

(no subject) - gjm11, 2006-06-22 11:46 pm UTC (Expand)

(no subject) - desh, 2006-06-23 06:23 pm UTC (Expand)

sermoa 2006-06-22 08:45 pm UTC (link)

Thanks for making this post - i find it all fascinating, especially all the comments and viewpoints that follow. Personally i wouldn't have thought the numbers were equivalent until i saw the 'multiply by 10, take it away, divide by 9' proof, which is very elegant and makes the point just perfectly. I believe the stumbling block for understanding is that it's so difficult to think about infinity. I started to think about if i was to say the number 0.99999recurring out loud, and realised that i would never stop repeating the number 9. NEVER! Even if i recited it for 70 years and then died, i still wouldn't have finished saying the number. In fact i'd have hardly started! That kinda boggled my mind a bit. (Reply to this)

That's wrong (Anonymous) 2006-06-22 11:25 pm UTC (link)

You say "0.9999... with an infinite number of 9s is equal to 1". I think this doesn't make sense. Some simple facts (well, opinions if you prefer :)): - Infinity is not a number, and "0.999... with an infinite number of 9s" doesn't mean anything mathematically.[1] - People are right when they say things like "I can always add a '9', I will never get to 1". - The mathematical notations "0.9999..." with the three dots, and "0.9" with a bar over the nine, are defined as limits (or series, a special case of limits). Here's a correct answer to this problem, in language (hopefully) understandable by non-mathematicians: The notation "0.9999..." is defined as the limit you are approaching when you consider the sequence of number 0.9, 0.99, 0.999, 0.9999, etc. Mathematicians DO NOT pretend that you will ever reach 1, they just say that you can get as close to one as you wish, provided you go far enough in this sequence.[2] Since in this case the limit is 1, we can say that "0.9999..." is just another notation for the number 1, in the same sense that "5 - 4" and "2*0.5" are different notations for the same number one. [1] Unless you use some arbitrary, non-standard definition of 'number' and/or 'infinity'. [2] This is actually a nice way to put in words the mathematical definition of a 'limit'. (Reply to this) (Thread)(Expand)

	Re: That's wrong (Anonymous) 2006-06-23 05:47 am UTC (link)
	There are some professions that must do tests to see if in fact what they are measuring does in fact reach one. These people do in fact work with very large and small numbers. (Reply to this) (Parent)

(no subject) - mivlad, 2006-06-23 07:32 am UTC (Expand)

	How people argue online (Anonymous) 2006-06-22 11:26 pm UTC (link)
	The point being: the more useless the argument, the more clueless the people, the more heated the debate will be. (Boycott slashdot, folks) (Reply to this)

_spider_ 2006-06-23 02:46 am UTC (link)

The idea that 0.9bar = 1 is an interesting one certainly. Intuitively the statement doesn't seem to be true, you've written down two clearly different numbers and claimed they are equal! But I suppose thats why I love maths so much, simple concepts like equality can be so easily misconstrued if you aren't following the rules properly, but if you sit down and think about it, it's really very easy to show (and has been in a number of different ways). Proof and Logic is one of my favourite topics in maths, and it's always very satisfying when you are able to relay a basic mathematical concept to someone else succesfully. Not to mention extremely challenging if you're dealing with someone who doesn't have the best grasp of maths. I look forward to the time when it's my job to do just that, argue maths with people. In the meantime, I'm enjoying learning more and more about the subject. (Reply to this)

	You're wrong marnanel (Anonymous) 2006-06-23 05:40 am UTC (link)
	.999 with an infinite number of 9s is not equal to one. It _approaches_ 1. It comes so close to one that for arguments sake (and we are arguing here) it for all practical purposes can be considered as 1. But it never, ever EQUALS 1. Ever. Sorry to burst your bubble. -- illogic-al (Reply to this) (Thread)(Expand)

	[dg] mivlad 2006-06-23 07:28 am UTC (link)
	What you say! (Reply to this) (Parent)

Re: You're wrong marnanel - marnanel, 2006-06-23 10:10 am UTC (Expand)

Re: You're wrong marnanel - phlebas, 2006-06-23 01:33 pm UTC (Expand)

Re: You're wrong marnanel - (Anonymous), 2006-06-23 04:29 pm UTC (Expand)

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(76 comments) - (Post a new comment)