Thread: 6÷2(1+2) = ? View Single Post
January 16th, 2013, 09:09 PM   #322 (permalink)
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Re: 6÷2(1+2) = ?

Quote:
 Originally Posted by mathman26 Oh, I know the principles and laws of reciprocity, etc And to me, 6/2n = 6 * (2n)^-1 Heh heh! That is exactly what I am saying. Order of operations: I am completely fine with. It is the things that you are operating on that I am also fine with, but many others are not. They are doing just that: Translating everything into an operator. 2x ? It is 2 x's. 2 cars? yup, 2 cars. We don't say "Hey, did you see the 2 times red cars drive by" ! It is a quantity, just like one mole of something, or a dozen. 24g ÷ 1 mole = 24g ÷ 6.022x10^23 not (24 ÷ 6.022) * 10^23 ab/cd ? (ab)/(cd) If I wanted abc/c, I write just that. same for (1/2)x, is x/2 1/2x? 1 ÷ 2x Just like (6/2)(2+1). I would write that, or i would say 6(2+1) ÷ 2 I apologize if it seems like a little rant I think it is saying "six divided by 3 x's" and not "6 divided by 3, times x" As I said, this was the intention of the meaning in 5 schools I went to. 6/3x is/was 2/x, otherwise you write 6x/3, or 2x Once again a ÷ 1a = ? We both know it is one, but we have brains for a reason, and we know the 1a is a single unit, which translates to 6 ÷ 2n, where '2n' is a single unit, and n is 2+1. I don't see how anyone can prove that a ÷ 1a = 1 and 6 ÷ 2a = 3a NOW.... we didn't use calculators in most of my school. It was all on paper, and calculators were forbidden, so we weren't victims of having to input it into a computer. I can't remember when we used them. We had to "prove" all work. When you realize how a computer/calculator interprets things, usually incorrectly, you end up putting ( ) around EVERYthing when you input. That said, it seems like our discussion is heading in the direction of, how would a computer interpret ..... ?? That is not where I wish it to go, as I care not what computer or program will come up with, or how they will handle the arguments entered. I am talking about: "Here is a sheet of paper. Solve this problem showing all work" Having said that, I would never be limited to same size characters on one line across and would hand-write something like this: ½ with a little 'n' right beside the 2. LOL !! Not another one !! I will pass on that one. I can tell you the first thing that comes to mind, but that is not my "final answer", Regis! Initial response is "no". not equal. If you use a limit, somehow, with summation and limit of f(x) as x approaching ∞, then the limit could be 1, obviously if f(x) was set up right. been a while since I was in school, so I would have to refresh all areas of that, and I am really not interested right now... I am almost finished with this one, and it was exhausting, but fun to get 'back in the books'. the annoying part was everyone calling everyone names, etc. Rarely did anyone provide a single reference. Speaking of refs, here is one: http://faculty.ksu.edu.sa/fawaz/481files/Bartle-Introduction-to-Real-Analysis.pdf Check out page 53 before and after "or more simply..." Regards! MM
Indeed. It more or less seems that our differing of opinions seems to result from my strict interpretation of the problem vs your logical interpretation of it combined with ambiguous notation. Since you noted that calculators were forbidden while learning this material (A stance I uphold in my own classroom), I have no doubt in my mind that if this was written in on paper that our opinions would result in the same answer. Indeed calculators are very helpful, but also very dumb at the same time. I think you are the first person I've come across here that actually cited analysis, other than myself. It tends to scare most people off.

As for the .999.... = 1 question, the thread was quite frustrating because most of the proofs for it require a higher understanding of infinite limits/infinitesimals. The true answer is that it is true as long as the .9 is infinitely repeating forever, but the arguments I saw in that thread were less mathematically based an more on feeling. You mentioned one of the ways to prove it in your response, taking the limit of a convergent infinite geometric series.

My analysis book is old, http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X/ref=sr_1_1?ie=UTF8&qid=1358393237&sr=8-1&keywords=mathematical+analysis+walter+rudin
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 Last edited by jhawkkw; January 16th, 2013 at 09:28 PM.
 The Following User Says Thank You to jhawkkw For This Useful Post: davoid (January 16th, 2013)