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#141
01-10-2006, 08:37 PM
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Re: .999~ = 1, Agree?
I'm tempted to give OOT a lecture on elementary real analysis, but I'll be good.
Mind you, constructing the field of real numbers isn't really that hard. A sequence of rational numbers is called a Cauchy sequence if... I'll be good. 
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#142
01-10-2006, 08:38 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
[ QUOTE ] It is irrelevant what level of math this is. To call someone pathetic simply for not grasping a concept is incredibly weak. [/ QUOTE ] Of course it's relevant. You can't expect everybody to understand hard university level stuff because not everybody has the opportunity or the motivation to learn it. However, there definitely is a point where the level of difficulty of a concept is low enough that it really should be common knowledge. Whether that point is above or below 7th grade math, I suppose, is up for debate. I'm of the opinion that 7th grade math should be common knowledge. Especially on this board. [/ QUOTE ] The problem with this post is that there is hard university level stuff underlying the basic algebraic proof. Given that, your seventh grader who votes yes is really doing nothing more than appealing to authority. It is reasonable for an intelligent person to hear the seventh grade explanation, question it, and not understand the deeper explanation. I bet if you were to ask 100 seventh graders whose teacher had just put the proof up the day before, the kid who still questioned it would be the smartest one in the room.
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#143
01-10-2006, 08:38 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
I'm tempted to give OOT a lecture on elementary real analysis, but I'll be good. Mind you, constructing the field of real numbers isn't really that hard. A sequence of rational numbers is called a Cauchy sequence if... I'll be good. [/ QUOTE ] Hehehe
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#144
01-10-2006, 08:42 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
[ QUOTE ] If that's commonly accepted definition of an infinite series, so be it. A definition is a definition. I was taught otherwise (I think - it's been a long time!), am I still a moran? To be honest, when I kept seeing 0.999...=1 everywhere, I thought all the writers of that were morans too, but was too polite to be rude about it. So I guess you win, huh? [img]/images/graemlins/grin.gif[/img] [/ QUOTE ] It doesn't make you a moron to be taught the wrong thing back in the day. You are also not a moron if you can change your opinion when faced with convincing evidence contrary to what you thought. The morons are the ones who, despite being shown clear evidence that they are wrong, still insist that they are right while not offering any solid reasoning why. You are not in that category. The ones in that category have stopped reading already. [/ QUOTE ] Yeah, I'm wondering if I was taught wrongly. I must have been - only a fool would say a definition is wrong - it's like saying dog isn't spelt d-o-g [img]/images/graemlins/smile.gif[/img] The funny thing is (and I say this to make a point, not to boast), I have a first class honours degree in Science (with biochem as a major element, but mainly in Ecology/Evolution), a PhD in computing/Ecology, taught maths to chemistry degree students, and this mistake never arose as an issue! Sorta shows (in those fields at least) how trivial/irrelevant it is in real life! [img]/images/graemlins/smile.gif[/img] I've gone from being pissed off to actually enjoying this thread. Learned something new and had some fun annoying mathematicians. Result! Thanks guys! [img]/images/graemlins/grin.gif[/img]
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#145
01-10-2006, 08:43 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
[ QUOTE ] Proof 1: 1/3 = .333333... 2/3 = .666666... 1/3 + 2/3 = .999999... = 1. [/ QUOTE ] tl;dr, but this "proof" sucks ass. [/ QUOTE ] Quoted for emphasis, the problem I've always had with this proof is that, while technically correct, it doesn't really help explain "why" .9~=1. If you are trying to prove/explain to someone why .9~=1 it isn't very helpful to assume 1/3=.3~ because if they understood that they would understand (in most cases) that .9~=1. For what are IMO better proofs refer to the wiki article on the subject (the advanced proofs section).
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#146
01-10-2006, 08:46 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
Sorta shows (in those fields at least) how trivial/irrelevant it is in real life! [img]/images/graemlins/smile.gif[/img] [/ QUOTE ] Pure mathematicians rarely are on the pulse of what is of practical relevance, even in serious science. Calculus worked just fine for the physicists for two centuries before the mathematicans came along and told them it was now OK to play with infinity.
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#147
01-10-2006, 08:48 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
The problem with this post is that there is hard university level stuff underlying the basic algebraic proof. Given that, your seventh grader who votes yes is really doing nothing more than appealing to authority. It is reasonable for an intelligent person to hear the seventh grade explanation, question it, and not understand the deeper explanation. I bet if you were to ask 100 seventh graders whose teacher had just put the proof up the day before, the kid who still questioned it would be the smartest one in the room. [/ QUOTE ] I don't think we need to bring university level math into this at all. 0.3~ is the decimal representation of 1/3. The 0.9~ = 1 thing doesn't even have any mathematical significance in our context. 0.9~ is an oddity of the decimal system that arises because the decimal system is not perfect.
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#148
01-10-2006, 08:48 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
Quoted for emphasis, the problem I've always had with this proof is that, while technically correct, it doesn't really help explain "why" .9~=1. If you are trying to prove/explain to someone why .9~=1 it isn't very helpful to assume 1/3=.3~ because if they understood that they would understand (in most cases) that .9~=1. For what are IMO better proofs refer to the wiki article on the subject (the advanced proofs section). [/ QUOTE ] Right, it begs the question, and as such IS NOT A PROOF AT ALL. [ QUOTE ] 1/3 = 0.333... 2/3 = 0.666... 1/3 + 2/3 = 0.999... = 1 [/ QUOTE ]
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#150
01-10-2006, 08:52 PM
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Re: .999~ = 1, Agree?
[ QUOTE ]
[ QUOTE ] The problem with this post is that there is hard university level stuff underlying the basic algebraic proof. Given that, your seventh grader who votes yes is really doing nothing more than appealing to authority. It is reasonable for an intelligent person to hear the seventh grade explanation, question it, and not understand the deeper explanation. I bet if you were to ask 100 seventh graders whose teacher had just put the proof up the day before, the kid who still questioned it would be the smartest one in the room. [/ QUOTE ] I don't think we need to bring university level math into this at all. 0.3~ is the decimal representation of 1/3. The 0.9~ = 1 thing doesn't even have any mathematical significance in our context. 0.9~ is an oddity of the decimal system that arises because the decimal system is not perfect. [/ QUOTE ] Not really. 9/10 + 9/100 + 9/1000 + ... = 1 whether we use a base 10 decimal system or not.
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