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mcc
Czech Republic4646 Posts
On April 08 2011 15:08 Cutlery wrote: View the 1/2x part of the poll to realize how most people interpret the / sign Its not even really about the / sign I think, it is by differently prioritizing implicit multiplication. | ||
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VIB
Brazil3567 Posts
On April 08 2011 14:34 Annoying wrote: Looks convincing.proof that answer = 2 If you have 48/2(9+3) The 2 is attached to the (9+3), anyone who even got past algebra should remember factoring an equation out. Example: 2(a+b)=2a+2b 2(9+3)=(18+6) From there you get 48/(18+6)=48/24=2 not my work but i don't see how can this be wrong. for proof, check out http://www.purplemath.com/modules/orderops2.htm 5th example. Could anyone of the 288 crowd link to an external source for the "algebric convention" people keep talking about? For any conventions that I've used during my whole life on work as a programmer, engineering college and primary school. The result is 2. | ||
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Tatari
United States1179 Posts
On April 08 2011 15:17 Turo wrote: Let (9 + 3) = x so 48/2(9 + 3) => 48/2x By the second poll, most people believe this to be 48/(2x) = 2. So why on earth is 288 leading? Good god. Do you NOT know the order of operations? Not only that, you really horribly twisted the problem around... 48÷2(9+3) Order of operations state that all calculations in parenthesis must be done first. 9+3 = 12 Therefore 48 ÷ 2(12) I'm praying that you also know that parenthesis can be used to symbolize multiplication. With that in mind... 48 ÷ 2 * 12 Order of operations state that multiplication/division come first before addition and subtraction. All calculation is done left to right. Multiplication does not have priority over division, vice versa. 48 ÷ 2 = 24 24 * 12 288 | ||
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MajorityofOne
Canada2506 Posts
-Eminem >.< this stopped being funny awhile ago, but keep it going and it'll prolly get funny again | ||
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Cutlery
Norway565 Posts
On April 08 2011 15:20 mcc wrote: Its not even really about the / sign I think, it is by differently prioritizing implicit multiplication. Ah, but when people see the / sign, they go with implicit multiplication. When they see the ÷ sign, the go with explicit. Two sides of the same coin. | ||
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Punic
United States152 Posts
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Musou
1375 Posts
On April 08 2011 15:09 mcc wrote: Ok that was bad example, I did not notice that it gets the same result in both notations. Let me rephrase I can define consistent notation where 48/2(3+9) = 2. Other than that it seems that you misunderstand what notation means and what your PEMDAS is. PEMDAS is not a law it is just a way of defining a notation. Let me state : 2 = * / 48 2 + 3 9 in polish notation (PEMDAS is not applicable) 2 = 48/2(3+9) in notation (lets call it NV) that assigns higher priority to implicit multiplication (PEMDAS is not applicable) 2= 16/2(2+2) in your standard notation (PEMDAS applies) 2 = 48/(2(3+9)) in both NV and standard notation 2 = 2 in all mentioned notations All those strings of characters mean the same thing : 2. NV is slightly different because it basically adds new operator - the implicit multiplication, but it just a virtual operator that you can easily get rid of by simple transformation using explicit multiplication and parenthesis. All those notations can easily be transformed into each other. Hopefully you can see how that transformation is done. Notations are just different ways to write the same thing, and they have different strengths and weaknesses. For example reason why Polish notation is so cool, is that it does not require parenthesis to make expressions not ambiguous, as it actually does not have them. Now math is not up to interpretation of notation. All mathematical laws are still in effect. All expressions have the same value, although their graphical representation(notation) might differ. PEMDAS is not a law, it is just a way of parsing an expression in standard notation and makes no sense in other notations. That can be seen especially well in Polish notation. Note that when I write 2+1=0 in Z3, that is not (just) different notation. In this case I am operating on different entities altogether. Of course you can create bunch of useless notations that are consistent, but otherwise serve no purpose. You could argue that NV is just such a useless notation (you cannot claim that about Polish notation and some others), that is your right. But as I pointed out it is often informally used, so it has at least some merit. Actually your interpretation of Polish notation (aka prefix notation) is incorrect. * / 48 2 + 3 9 is done using a stack, so you would push * then / onto the stack and find 48 and 2 for the operands for the current operator /. The equation then becomes * 24 + 3 9, then * 24 12, then 288. It would never equal 2 using PN. | ||
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mcc
Czech Republic4646 Posts
The point is that it depends on chosen notation. | ||
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Ruyguy
Canada988 Posts
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Tatari
United States1179 Posts
On April 08 2011 14:34 Annoying wrote: proof that answer = 2 If you have 48/2(9+3) The 2 is attached to the (9+3), anyone who even got past algebra should remember factoring an equation out. Example: 2(a+b)=2a+2b 2(9+3)=(18+6) From there you get 48/(18+6)=48/24=2 not my work but i don't see how can this be wrong. for proof, check out http://www.purplemath.com/modules/orderops2.htm 5th example. God. This irritates me to no end. Do some people not get anywhere with basic math education? The only reason why you distribute is because there is a variable (in that case, x). The reason why you don't do that in here is because all the numbers have known values and you apply the order of operations instead of screwing around. | ||
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Turo
Canada333 Posts
I'm taking math in Uni right now, and really this is a worthless question. EDIT: not your question xD, the OP's question. 1 - Notation isn't about who can follow the rules the best, it's about clearly conveying the information. If the information isn't clearly conveyed, then it's the failure of whoever wrote it, not who is reading it. 2 - No one would ever write something down like this. There's a reason math is all done by hand, everything is much clearer. (fractions etc.) 3 - This SHOULD have the appropriate brackets. Once again, it's not the failure of the reader, it's the failure of the WRITER, who did not make his/her notation clear. | ||
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mcc
Czech Republic4646 Posts
On April 08 2011 15:25 Musou wrote: Actually your interpretation of Polish notation (aka prefix notation) is incorrect. * / 48 2 + 3 9 is done using a stack, so you would push * then / onto the stack and find 48 and 2 for the operands for the current operator /. The equation then becomes * 24 + 3 9, then * 24 12, then 288. It would never equal 2 using PN. Oops, was concentrating on getting NV right and just copypasted Polish one from previous post. You are of course right, should be for example 2 = * / 48 48 + 1 1 | ||
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Tatari
United States1179 Posts
On April 08 2011 15:27 Turo wrote: 2 - No one would ever write something down like this. There's a reason math is all done by hand, everything is much clearer. (fractions etc.) Well, someone did indeed write something down like this. That is, the person who came up with the question. Jus' sayin'... | ||
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Capook
United States122 Posts
 . Obviously, it's a matter of convention. However, since programming languages would give 2, and math people would say "notation is ambiguous" or "you're an idiot for trying to use this kind of notation", I think 2 is the clear winner, and has my vote, as an upcoming physics phd. | ||
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Turo
Canada333 Posts
On April 08 2011 15:30 Tatari wrote: Well, someone did indeed write something down like this. That is, the person who came up with the question. Jus' sayin'... No one who was serious about their work, in my opinion. I believe the division sign stopped being used around elementary school. I don't think it should even be taught lol | ||
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VIB
Brazil3567 Posts
On April 08 2011 15:27 Turo wrote: Best post in the thread. imhoI'm taking math in Uni right now, and really this is a worthless question. EDIT: not your question xD, the OP's question. 1 - Notation isn't about who can follow the rules the best, it's about clearly conveying the information. If the information isn't clearly conveyed, then it's the failure of whoever wrote it, not who is reading it. 2 - No one would ever write something down like this. There's a reason math is all done by hand, everything is much clearer. (fractions etc.) 3 - This SHOULD have the appropriate brackets. Once again, it's not the failure of the reader, it's the failure of the WRITER, who did not make his/her notation clear. When you are writing it down you use fractions to make it clear. When typing it on a program, you use parenthesis. The OP is missing both and is then, ambiguous. | ||
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iSTime
1579 Posts
On April 08 2011 15:27 Turo wrote: 2 - No one would ever write something down like this. There's a reason math is all done by hand, everything is much clearer. (fractions etc.) . I hear latex is pretty sexy. | ||
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WGarrison
United States96 Posts
If we did a math problem with (1/2)x, we would not type it as 1/2x but as x/2 instead. So 1/2x gets interpreted technically incorrectly but is often written technically incorrectly as well. Two wrongs make a right haha. 1/2*4 will get interpreted correctly as 4/2 or 2 much more often than 1/2x. | ||
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Turo
Canada333 Posts
xD too bad this ain't latex! | ||
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chonkyfire
United States451 Posts
48/24=2 I'm a 288er switching to 2 | ||
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