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04-30-2011, 10:40 PM | #91 (permalink) | ||
carpe musicam
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When one takes the problem 6/2*(1+2) 6/2 could be seen as a fraction (as six halves) or the equation 6÷2 in either case the parentheses are not the problem, both will equal "9." If one take into consideration it is a fraction, it only yield "1" when one considers 2*(1+2) the denominator as a coefficient of (1+2), and one ignores the numerator as also a coefficient of (1+2). And it one considers 6/2 as 6÷2 then the problem 6÷2(1+2) or 6÷2×3, it will only yield "1" when one does not follow convention and doesn't do operations from the left to the right. One the about Math is that one can tackle a problem six ways to Sunday and still end up with the correct answer provided if one follows proper procedure and convention. If you take consistency and convention out of Math, and make things in it relative you will have 2+2=5.
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"it counts in our hearts" ?ºº? “I have nothing to offer anybody, except my own confusion.” Jack Kerouac. “If one listens to the wrong kind of music, he will become the wrong kind of person.” Aristotle. "If you tried to give Rock and Roll another name, you might call it 'Chuck Berry'." John Lennon "I look for ambiguity when I'm writing because life is ambiguous." Keith Richards |
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05-01-2011, 05:23 AM | #92 (permalink) | |||||
Dat's Der Bunny!
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Neapolitan, that is impressive. You have again quoted one of my posts, completely failed to read it, and restated your argument.
Mathematics is not always consistent. If it is defined properly and is being used within the bounds that have been shown to be consistent, then yes, it is consistent, but it is not magically always right. Quote:
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What you stated about Schrodinger's Cat means either you misunderstood the point I was making, or you are claiming that the Cat will always be dead or always be alive when we "open the box". i.e, when parentheses are added (giving the necessary information to find a unique answer) the answer will always be 9. Which is, as I have proven multiple times in this thread, completely wrong. Quote:
[QUOTE]If one take into consideration it is a fraction, it only yield "1" when one considers 2*(1+2) the denominator as a coefficient of (1+2), and one ignores the numerator as also a coefficient of (1+2). [QUOTE] I actually have no idea what you're saying here. I'll happily address it if you want to explain what you mean, but I would imagine that it doesn't really affect the overall verity of the post. Quote:
Can you prove your convention is correct from Base Principles? If you can't, then it's not a mathematical constant, it is simply a convention, and a non-standard one at that. A common one, yes, but nowhere near universal. "One thing" about Maths is that when it is taught at 1st and 2nd level, a lot of shortcuts are taken in order to make it easier to teach. "Rules" are given so that the concept of ambiguity can be avoided, because maths is difficult enough when people are sure that there is one right answer. Your final statement about 2+2=5... well, I've already addressed that point. Until you can show me an axiom which states the order of operators (even only defined on the Field of Real Numbers), that argument is invalid. @Tuna: Quote:
I would like to remind anyone still arguing this that I'm not saying that your answer is wrong. By all means, it's the most popular way of solving the equation. It's just not Syntactically correct, which means that even though the most common convention states that the first pair of parentheses can be assumed around (6/2), it is an assumption, and so long as they are not there, you can claim that the = 1 answer is just as correct. @Freebase: That's part of what I'm saying, certainly. It's more that nothing in maths can be taken to be certain unless it is defined that way, given as an axiom (a statement so obvious that it cannot be proven), or provable from the definitions and axioms. Nowhere in any of the axioms that I have been taught regarding the Real Numbers (the number line, essentially) is there an axiom or a definition which states the universal order of priority of operations. There is a standard, which is almost universal, but as is evident from this thread, not entirely so. That's what my point boils down to, that a convention that is not a definition, not universal and not provable from the axioms is being taken as irrefutably true. @CanwllCorfe: I understand your belief, but I'm afraid that it's as a result of the way maths is taught: Certainly among at least 50% of the population of at least the western world, you would be safe in making such assumptions, but mathematics is not a subject where you can say "because it holds for the majority, it holds for all". Indeed, there are still some theorems out there that remain unproven even though we know that it holds for every case that we can possibly calculate, just because we can't prove it for a general case. Does that make sense?
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"I found it eventually, at the bottom of a locker in a disused laboratory, with a sign on the door saying "Beware of the Leopard". Ever thought of going into Advertising?" - Arthur Dent Last edited by MoonlitSunshine; 05-01-2011 at 05:30 AM. |
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05-01-2011, 06:46 AM | #93 (permalink) | |
Mate, Spawn & Die
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05-01-2011, 07:44 AM | #94 (permalink) |
Dat's Der Bunny!
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And generally, that's fine, as multiplication and addition are associative operations (it doesn't matter what order you do them in). It's where there's ambiguity over which elements the inverse is being applied to that there's a problem.
Consider a situation where you have a/b/c. Is that (a/b)/c, or a/(b/c)? take an example, 2/3/4. (2/3)/4 = 2/12 = 1/6, but 2/(3/4) = 8/3. The two answers are very, very different, but how do you define which one is the fraction? Which equal priority operation needs to be done first? The same problem holds when you have a/b*c. Is that (a/b)*c, or a/(b*c)? The fact that most people assume it is (a/b)*c does not make the syntax any more correct: If someone writes "I hae that" you could assume they left out a t or a v; depending on which it is they've left out, it makes a big difference to the meaning of the sentence, but you can usually figure out which they mean by the context of the sentence. It doesn't however, make the sentence, if isolated from the context, any less ambiguous. Does that make sense?
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"I found it eventually, at the bottom of a locker in a disused laboratory, with a sign on the door saying "Beware of the Leopard". Ever thought of going into Advertising?" - Arthur Dent |
05-01-2011, 08:01 AM | #96 (permalink) |
Dat's Der Bunny!
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Wolfram Alpha would be a more acceptable God, but I guess beggars can't be choosers :P However, I refer to the "why google gives 9" argument regarding choosing the most common convention to solve the ambiguity. Calculators are programmed to add parentheses on a left to right basis if the user has not entered a sufficiently unique statement.
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"I found it eventually, at the bottom of a locker in a disused laboratory, with a sign on the door saying "Beware of the Leopard". Ever thought of going into Advertising?" - Arthur Dent |
05-01-2011, 08:04 AM | #98 (permalink) |
Dat's Der Bunny!
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...you guys are just deliberately trying to annoy me now, aren't you :P
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"I found it eventually, at the bottom of a locker in a disused laboratory, with a sign on the door saying "Beware of the Leopard". Ever thought of going into Advertising?" - Arthur Dent |
05-01-2011, 08:16 AM | #99 (permalink) | |
FakingSuicideForApplause
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