KLB

For me this is what helped me get the idea that 0.999.... = 1. On the face of it this isn't logical but the simple fact that by some convention 1/3 = 0.3333..... and that 0.33333.... must be carried to completion to equal 1/3 and that 3 times 1/3 equals 3/3 which equals 1, then 3 times 0.333333.... equals 0.9999..... which by convention must equal 1. It's a freaking mind trip, but it is hard to argue against: 1/3=0.3333.... +2/3=0.6666.... --------------- 3/3=0.9999.... Since 3/3=1 then 0.9999.... must also equal 1. I see no way to argue against this. I'm no math whiz and I stated up front that I didn't believe that 0.9999.... equaled 1, but I can't argue against the equation above or point to a flaw in its logic. It is a very simple equation and there are no crazy x=y tricks to confuse me. The result seems very counterintuitive to me, but everything adds up, so it must be true. Somebody show me where the logic flaw or math error is in the example I gave. Excuse me while I go wander off to fix the cogs I broke in the ol brain trying to grasp this stuff.

No I was only speaking for myself that I tend to question EVERYTHING. I'm not as bad as my brother, but rarely take anything at face value. My brother was so bad as a kid that if you told him a pan was hot he'd touch it to see for himself. While I don't advocate touching a hot pan to verify that a pan is hot, I do advocate questioning something that one doesn't understand. As I did here in a round about way. As you can see by my post above, in part because of this thread, I was able to work through the logic and see how 0.999....=1. It really messed with my mind, but I do now understand. I like understanding why something is the way it is. It helps reassure me that I'm not accepting something on blind faith. This whole thread actually has been really cool and I learned something really weird. Who knew that math could stir up so much debate or have such interesting quirks.

Based on the proof I posted in post #33 I see how 1/3=0.3333... so 3/3=0.9999.... thus 1=0.9999.... Really, 0.3333.... is just a decimal representation of a fraction 1/3 and 0.9999.... is just the sum of three 0.333.... added together and since the sum of three 1/3 is 1 0.9999.... must equal one. In a way I guess it is just a convient convention to clean up a messy little quirk. It makes sense to me now, but man what a mind trip. Now if someone decides to use something like this in real life rather than rounding to significant digits I'm going to smack them. See people helped explain it in a way that someone who hasn't touched a math book since college could grasp the concept and thus accept the logic. Now if we could just do the same about certain biological concepts.

Okay, I looked up the definition of "real number". The easiest to understand definition was "a real number is any number which can be represented as a non-terminating decimal." This is from http://www.filosofia.net/materiales/rec/glosaen.htm So great, a real number is any number best I can tell. I looked up non-real number and couldn't get a definition. I then relooked at the blog entry first referenced with all the proofs and broke a few coggs in the gear box. For instance: 1/3=0.33333.... +2/3=0.66666..... ============= 3/3=0.99999..... I see it and I agree with it, but my mind can't make it make sense. My sense of reality feels like it has been shattered.

My point was simply that we must always question everything. I'm going to go back to my finite mind, but to me an infinitesimally small number is approaching but never quite reaching zero. Simply put I'm stuck on Bascule's example that no matter how far one carries it out, when one stops one always ends up with a difference of 1^-n. I'm not going to take it as an insult. I mean after all my math skills were molded in the U.S. education system. My purpose of participating in these forums is to learn and grow, I can't do either without stretching my mind and this thread is really stretching my mind.

Well I think this thread is proving your point. This is the problem I'm having a hard time overcoming. My poor finite mind is really tying itself in knots trying to grasp this. Sorry but this runs against my inclation not to accept something to be fact without questioning. I also think that we are better off having mind numbing discussions trying to prove to someone like me that 0.99999.... = 1.000.... than we are having people blindly accepting what "experts" tell them without question.

This thread is moving faster than I can keep up, so my posts will be lagging a few posts behind the post they are referring to. The point of my first post wasn't to support or disprove .9999.... = 1. The point was to try and answer the question why threads get so nasty so fast. The worst mistake any one can make is to not question an "expert". The moment one declares that they are an expert, one must begin to question. Case in point, the Pope is supposedly an expert on God. If we aren't to question experts, then we shouldn't have question Popes when they told us that God created the world in six days. Supposed experts told us that there was definitive proof that there were WMD in Iraq yet none were ever found. The reasoning and proofs of experts in the math and sciences have been turned on their head throughout history. We can only try to get to the truth by questioning. Too often threads turn into personal attacks because "experts" take offense at being questioned. If an expert is truly an expert then they should have the confidence not to take the questioning of their knowledge personally and try to explain something in a way those questioning can understand. Otherwise it looks like arrogance, which doesn't help dispel bad information. Only a fool does not question. In the sciences, "experts" must get over the arrogance of saying take the time to learn to those who question and doubt and instead learn how to explain things in a manner that the common person can understand. Unless this is done, the debate over things like evolution vs. creationism will go on for all eternity and we will be forever having to battle to keep the various forms of creationism out of the science classroom. At the very least without questioning, one does not learn. Who knows, today I might learn more than I really cared to learn about numbers. Two hours ago I, if someone would have told me that 0.9999...=1.000... I would have told them they were nuts. Now while, I may not fully see how .9999....=1, I do see how 1.0000.... - 0.9999.... = 0.0000.... Still, best I can grasp is that the difference between 1.0000.... and 0.9999..... is infinitesimally small, but it is not 0.

Okay how about if it were written like this? 1.00000.... minus 0.9999... equals 1^-n where n equals infinity. The question is what is the purpose in trying to prove this one way or another? Does it really matter? For human uses, no matter how percise we needed to make a calculation, eventually we would determine the number of significant digits and round off which would mean that for our purposes 0.999... would equal 1.

To me these types of statements are efforts to downgrade the validity of others by questioning their intelligence or education and by using grandiose jargon designed to make one's self look like a learned expert who should not be questioned. This may not be the case here; however, it is a classic "debating" stunt that is used constantly in forums and on TV news programs. These types of comments in threads aren't designed to support one's stance by helping others to understand one's position better; rather they are designed to discredit the stance of others. It is these types of arguments that spark hostile and personal exchanges that ruin good debates/discussions. If you believe that .9999....=1 then prove it in a fashion that others can understand and accept even if they were educated in the U.S. educational system and hasn't had to deal with proofs for twenty years. Again these types of arguments go back to my first comment in this reply. Insulting others is what drives threads down and it is a typical tactic use to discredit others in so many discussions. It is also a very commonly used tactic by those who can't really argue for their position. In a discussion that is either true or false like .9999....=1, one shouldn't need to insult others or use confusing logic to explain why something is or isn't. From a practical stance, .9999.... would close enough to equal one; however, given the limits of my U.S. education, the best I understand about numbers is that no matter how far out one carries .9999.... it will always be .00001... short of 1. Put another way we would all agree that 1=1.0000.... and 1.0000.... !=0.9999.... Again the difference would always be 0.00001.... (or however you want to note it) In reality, I don't see how it matters if .9999....=1 or not; the point of my post was to show why threads like this get drawn down into nasty exchanges on a regular basis.

Okay I'll be part of the crowd that believes that those who believe .999....=1 are either smoking crack or are trying to screw with my head and I've seen too many "proofs" drawn up that try to prove to me that 1+1=3. In general all of this stuff makes my head hurt so I won't dive into the merits of the proof. In regards to Sisyphus's question about the hostility, I think we could create a thread on just about anything and it would turn into hostilities. I've seen it happen way to often in way too many forums (I visit/participate in around 1 dozen different forums). The simple fact of the matter is that people seem to mistake hostility and personal attacks with reasoned debate and I blame this on things like FOX News. I honestly think that reasoned constructive debating is a dying art form as is being able to accept and acknowledge valid points from opposing sides of an issue. There is no effort to find a middle ground or listen to other points of view. People simply want to ram their viewpoint down the throats of others. Look at the 9/11 thread that got closed a couple of hours ago.

This is a very solid argument as to why the war is not sustainable. Keeping us bogged down in a protracted war is a good way terrorists/insurgents can weaken us. Every billion dollars spent on this war is a billion dollars that can not go towards more constructive ends that make our own country better. The only one's benefiting from this war is the military industrial complex (e.g. Brown & Root and Haliburton).

I'm using Avast but have never used AVG. I am very happy with Avast. It is much better than Symantec NAV which I used to use.

There was a really good Frontline episode on PBS this evening entitled "The Dark Side" about all of the intelligence used to draw us into a war with Iraq and how Dick Cheney and Donald Rusfeld used unvetted intelligence to push their case even when the CIA said that the intelligence was flawed or the CIA provided proof that what Dick Cheney and Donald Rumsfeld were claiming was wrong (e.g. the tie between al Qaeda and Saddam). For those who didn't see the episode, it can be watched online at http://www.pbs.org/wgbh/pages/frontline/darkside/. There is also a lot of supporting information online as well. This also provides very good evidence that justifies my use of "false pretenses" even in the strictest definition of the phrase.

Then it probably won't be annoying to them as the noise is designed to become annoying if one is hanging out for a period of time. If they are in an area long enough for the sound to become annoying then in all likelyhood they are loitering. If a store is only having a problem with teen loiterers why should they subject others to the noise? The goal is to stop loitering. If teens were respecting the no loitering signs then there wouldn't be a market for these devices. Now obviously if a store is having a problem with adult loiterers this technology will do no good and a different solution would be needed. The point is that this technology is just another tool stores can choose to use to reduce loitering. For some stores it will make sense for other stores it will not.

I'll agree that it was a political stunt for this fall's elections. I personally don't think this was a serious debate. Call me cynical if you want, but to me it was nothing more than cheap political stunt and provided no real value to the overall debate about when and how we extract ourselves from Iraq. Have a good vacation.

I do not accept Wikipedia as a legitimate reference source for writers who contribute to my environmental chemistry site and I won't accept it as a reference source here. Their posts are created by anonymous persons who can post anything they want regardless of their qualifications. References or no references any scientist knows that without editorial control and full disclosure a source should not be relied upon. I have provided multiple sources for the definition of "pretense" (and provide multiple sources for "false pretenses" below). You are continuing to rely on only one unreliable source that fits your narrow view of the word. As with other English words and phrases, "false pretenses" is not defined by one very narrow definition, rather there are a range of definitions and similar meanings. I stand by what I said. WE WENT TO WAR UNDER FALSE PRETENSES. Members of Bush's administration declared on multiple occasions that had irrefutable proof that Saddam had WMD and Donald Rumsfeld went so far as to state he knew where they were. As no WMD has ever been uncovered since the invasion, obviously there is no way Mr. Rumsfeld could have known where the WMD was because they did not exist. Collin Powell claimed Saddam had mobile biological weapons labs, yet even when he was making these statements the intelligence community was questioning this. Furthermore Dick Cheney repeatedly tried to create links between Saddam and Bin Laden that did not exist. This means that even by your strict definition of "false pretenses" we went to war under false pretenses. The Bush Administration dragged out all kinds of trumped up half baked intelligence to show that Saddam had WMD yet all indications are that Saddam had not had ANY WMD programs since at least the late '90s. This means that the vast majority of the intelligence used to justify our going to world was faulty yet we were assured that it was irrefutable. This again supports the claim that we went to war under false pretenses. The reality is that Saddam cared more about staying in power than he did developing WMD and thus he probably abandoned his WMD programs so as to deny the U.S. an excuse to invade. If this Administration was going to invade another country, ask our soldiers to die and cause the death of innocent civilians via "collateral damage", then the Bush administration should have exhausted every intelligence source and make sure that the reasons for going to war were true. This obviously wasn't done or they would have quickly learned the sources they were relying on were faulty. A failure to properly validate intelligence used to justify going to war DOES NOT exonerate the Bush Administration from the fact that they took us to war under false pretenses. Dick Cheney repeated tried to create connections and relationships between Saddam and Bin Laden that did not exist. No reasonable intelligence found that there was a connection. In other words Dick Cheney tried to misrepresent facts so as to gain support for going to war with Iraq as part of the larger war on terrorism. When using Merriam-Webster, dictionary one must look at the definition of each word, which is what I did. Again I stand by my interpretation of how to use the word pretenses. Regardless of how much you want to argue the Queens English usage of "false pretenses" my usage was reasonable and appropriate as I used it in this thread. You can choose to substitute some other word in your mind if you want, but based on the definitions I posted and my justifications I will continue to use the phrase "false pretenses" in regards to President Bush taking us to war. It is an accurate description of what happened.

Descrimintation in the business sense refers to refusing to do business with a specific group of people or refusing to hire a specific group of people. In this case by definition loiterers are neither customers nor employees so even if only a specific group can hear the sounds it is not descrimination. By loitering one is already breaking the law if the store has posted a sign that states no loitering. Also as has been pointed out several times in this thread, the method of using high pitched sounds that only teans can hear are designed for businesses who are having problems with TEEN loiterers. If only teens are loitering why should a business use a sound that everyone can hear.

Okay I misunderstood your intentions. First I would think that people in this forum above all others would understand the reasons why Wikipedia should not be used as a reference source. Heck even the New York Times doesn't allow Wikipedia to be used as a reference source. The more I think about my usage of "false pretense" the more I think it was totally appropriate in this case. If for no other reason than there are more definitions to pretense and thus false pretense than you will allow. I'm going to nitpick your narrow definition of pretense and show that my usage is not incorrect: Google search "Define:pretense" http://www.dictionary.net/pretense 1. The act of laying claim; the claim laid; assumption; pretension. --Spenser. http://www.thefreedictionary.com/pretense http://www.answers.com/topic/pretense 6. A right asserted with or without foundation; a claim. http://encarta.msn.com/dictionary_/pretense.html 2. unwarranted claim: a claim, especially one with few facts to support it http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=pretense (Merriam-Webster) 1) a claim made or implied; especially : one not supported by fact Note the last definition "a claim made or implied". Yes false pretense especially applies to claims made that are known to be false, but it can also be used for claims that turn out to be false as was the case with the WMD claims. Bush may have believed his claims about WMD. He may still believe that Saddam had WMD; however, the fact is that no WMD have been discovered in spite exhaustive efforts to turn them up and claims made by Donald H. Rumsfeld in press conferences that they knew where the WMD were. You can argue all you want about whether it was intentional or simply being blind to intelligence that refuted the claims being made; however, the Bush administration via Collin Powell asserted to the UN Security Council that Saddam had WMD and that he was harboring al Qaeda. As it turns out these assertions were without merit or foundation. In fact by all accounts the claims that Saddam was harboring al Qaeda was known to be untrue from the beginning but the Bush Administration tried to use the thinnest of evidence to convince the world otherwise to help justify a war they had already decided to undertake before 9/11/01. According to an interview given by President Clinton around the time of the opening of his Presidential Library, the same group that convinced Bush to invade Iraq had also tried very hard to convince Clinton to do the same thing but he refused because he didn't have strong enough intelligence to justify such an act. The Bush Administrations assertions were made based on bad analysis of intelligence, bad intelligence from unreliable sources and the ignoring of intelligence that led to conclusions that were contrary to what the Bush Administration wanted to see. Did Bush him self know that the information was false? Maybe not, but they took what information supported the reality they wanted to believe in and discarded the rest. They deceived themselves and the rest of the world. We went to war under the false pretense that Iraq posed an imminent threat. When laying out the reasons for going to war with Iraq, the Bush Administration had an obligation to question and vet all intelligence that was being used to support those reasons and to make sure the intelligence was factually correct, they also had an obligation to question the motives of the sources providing the intelligence. They did not do this. They even included intelligence that was known to be faulty in the State of the Union address (the attempts to by yellowcake uranium from Niger). In the case of the yellowcake incident, it would not have taken very much digging or fact checking at all to realize that the information was not reliable. This fact checking, however, was not done. Just because the Bush Administration might be able to claim they did not know the intelligence was bad does not excuse their actions. They should have known how reliable the intelligence was that they were using. In fact they had an obligation to make sure that they didn't just have evidence, but that they had irrefutable proof. There was a willful decision not to properly vet intelligence that supported beliefs that we should go to war with Iraq. This is no better than out right lying and should in this case be considered the same thing. I understand this but I stand by the usage of the term "false pretense" because our pretense for going to war was that Saddam had WMD, was trying to acquire nuclear material and was harboring al Qaeda. The justification for going to war was based on false intelligence provided by unreliable sources thus we went to war under false pretenses. No doubt the things you quoted were some very horrible acts, but the UN Security Council would not have supported any invasion of Iraq for these reasons alone. They only supported our invasion of Iraq because of the WMD claims and the claimed links to al Qaeda. Immediately after 9/11 those attacks and the war on terror were the Bush Administration's trump card to justify our right to self defense. It was because of the claims about WMD and the links to al Qaeda that the UN Security Council did not stand in the way of invading Iraq. The other reasons were nothing more than secondary considerations.

I'm sorry but supporting one's policy to go to war based on what should have been known to be bad intelligence is false pretenses. A classic example of this was the Administrations claim that Iraqi had attempted to purchase yellowcake uranium from Niger. Yet this was based on forged evidence and the validity of that information had been brought into question long before the administration used this as part of their justification to go to war. On the surface, this intelligence supported the desired objective so the intelligence was not questioned. Failure to question the intelligence on an issue that is as important as this is unforgivable. No, I just think that you can't defend your position on the issues so you have to nitpick semantics. This is a classic debating tactic.

In a statement to the Security Council of the United Nations Collin Powell provided what was call irrefutable evidence that Iraq had weapons of mass destruction and mobile biological weapons labs and was a clear and present danger to the US. Iraq was also accused of harboring al Qaeda terrorists. In fact NO evidence has ever been found that Iraq had weapons of mass destruction and those "mobile weapons labs" turned out to have no ability to produce biological weapons and were for peaceful purposes. Furthermore alQaeda was not being harbored by Sadam and they did not gain a foothold in Iraq until after the U.S. invaded. We can argue whether or not it was faulty intelligence or intentional misrepresentation of the evidence, however, the fact is that the reasons for going to war were false. It was only after the reasons were found to be false that the reasons for going to war shifted from Iraq being an imminent threat that the reasons for going to war were shifted to liberating Iraq and bringing them Democracy.

D'oh! Editing error. I should have typed "While I DON'T like". I'll fix that. I did not say I want to know that it exists. I said that I HOPED it would exist. Don't read what isn't there.

I did not read that into his post. Pangloss MAY simply be indicating that he does not feel that we have enough information to pass judgement. I personally DON'T like the fact that we went to war under false pretenses. I also don't like the way war has been handled (e.g. not overwheming forces to inforce a peace). I would not, however, advocate walking out of Iraq tomorrow, nor would I advocate a publically announced timeline for withdrawl. I would hope that there was such a plan in place and that this administration had a clear plan to get us out of there as soon as possible, but I would not want it publicized. There is no sense letting the insurgents know they only need to lay low for awhile until we are out of there. --edit-- Fixed an editing error and added the word DON'T

My feeling is that a timetable may be important for planning purposes, but that it should not be shared with the world. I do not like this war, I think we were lead to war under false pretenses, I think the current administration has been lying to us throughout the entire war and I think we need an exit strategy. I also believe, however, that publicizing our exit strategy and time table could do more harm than good. The house vote was also wrong because it was done as a political stunt to create campaign fodder for this fall's election. It was not about creating a sound policy in regards to the Iraq war.

Accidental double post. Sorry

I just wish people would see this vote for what it was a meaningless political stunt to distract attention and score a few points for this fall's elections. It means nothing, it does nothing, it is non-binding. I wish voter's would wake up and punish politicians who pander using cheap do nothing political stunts like this. The marriage amendment falls into the same lines. Instead of spending time writing and passing legislation that could make people's lives better and actually solve problems, politicians waste time on things that mean nothing and do nothing.