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Thread: Mathematics and precedence rules

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Re: Mathematics and precedence rules
...Is Zaire a place?
See, I can do math, but nobody ever taught me geography.
On a completely random note, I actually think that mathematicians are more likely to disregard trivial stuff and write in absolutely ambiguous manners. I can't count how many times I wrote
log x+2
to mean log (x+2) and
log x + 2
to mean (log x) + 2 on my exams for courses like probability theory.Jude P.
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Re: Mathematics and precedence rules
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Re: Mathematics and precedence rules
Heliomance: You win.
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Brian P."Opportunities to do good are everywhere but the darkness is where the light needs to be".
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Re: Mathematics and precedence rules
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I know, see my earlier post  you should always use Scientific mode, which does it correctly. Windows Calculator in Standard mode will do it incorrectly regardless of brackets, Windows Calculator in Scientific mode will do it correctly regardless of brackets.
This. Exactly this.
The equation is not in any ambiguous, and no amount of claiming it is so will change that. If you know and follow the very clearly defined, internationallyagreed upon procedure for the order of operations, you will always get the same answer. There is absolutely no point where something could be one thing or the other, by following the rules correctly, you will always know what to do and always get the same answer.
The original poster on Facebook observed that some people were not following the rules taught in basic maths to complete this equation and released it into the wild to trap them, but that does not make it in any way ambiguous!
It's not like the sentence "Bob met Fred at the train station, he had recently had a haircut." where either Bob or Fred could have had the haircut. Correct rules of maths dictates that it must be one particular way.
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Re: Mathematics and precedence rules
Doesn't the right side end up as 2 while the left side ends up as 1?
I vaguely suspect, if my previous statement isn't wrong, that it should be a z and not a 2 in the exponent inside the first limit so that it ends up as e, whose Neperian Logarithm is 1, making the left side 1+1.Last edited by araveugnitsuga; 20121011 at 08:15 PM.
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Re: Mathematics and precedence rules
I know, see my earlier post  you should always use Scientific mode, which does it correctly. Windows Calculator in Standard mode will do it incorrectly regardless of brackets, Windows Calculator in Scientific mode will do it correctly regardless of brackets.
If you know and follow the very clearly defined, internationallyagreed upon procedure for the order of operations, you will always get the same answer.
Respectfully,
Brian P.Last edited by pendell; 20121011 at 08:26 PM.
"Opportunities to do good are everywhere but the darkness is where the light needs to be".
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Re: Mathematics and precedence rules
On rechecking, you are in fact correct, due to ln(1) = 0. I don't think changing the 2 to a z would do anything useful, the easiest way to fix it is to get rid of the ln.
The other problem is that it's mixing matrices and real numbers  it really needs to take the determinant of (X^1)^T(X^T)^1.

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Re: Mathematics and precedence rules
Changing the 2 to a z would produce the limit's definition of e [limit of ((1+1/z)^z) as z tends towards infinity], which, inside ln, would produce 1. The only issue with the matrices is if they can in fact be inverted, otherwise it does work since the inverse of the transposed is the transposed of the inverse if the original was invertible.
So if you take that X is an invertible matrix as a hypothesis and replace the 2 in "limit of ((1+1/z)^2) as z tends towards infinity" with a z it does add up.
I'll also note Wolfram Alpha can't solve this, due to being unable to reason out through properties that the most complex calculations cancel out without needing to be performed.Last edited by araveugnitsuga; 20121011 at 08:46 PM.
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Re: Mathematics and precedence rules
The average math SAT score is not the average score of the population. It is the average score of those who take the SAThigh school students who plan on attending college. A substantial minority of people do not take the SAT, such as high school dropouts and high school students with absolutely no interest in college. Therefore, the actual average is likely lower.
Second, most people get SAT math questions wrong because of careless mistakes in a time sensitive test. The actual concepts are designed to be accessible because it is an aptitude test, not a test of one's math education.
The math section tests for speedespecially with problems that aren't hard conceptionally but require time to solveand attention to detail more than actual math concepts.

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Re: Mathematics and precedence rules
If you wrote that equation for people who know basic maths, then there is absolutely no reason to change it. If you wrote that equation as a test to see if people know basic maths, then there is absolutely no reason to change it. If you wrote that equation for people you know don't know basic maths, then you should not have written that equation at all, not without at least a paragraph explaining where Zaire is, what its capital is, and why it's important.
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Re: Mathematics and precedence rules

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Re: Mathematics and precedence rules
Oh, forgot...
Just stick a "det" to the right of the parenthesis, add another layer of parenthesis to indicate factorial of determinant and it does work out. Which is what you originally suggested.
And this is why parenthesis are really needed, in order of operations they are just trivial (and well, for playing around with a negative sign in front of parenthesis), for slightly more complex things it's to make things make sense (and exponentiation of grouped terms)Last edited by araveugnitsuga; 20121011 at 09:01 PM.
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Re: Mathematics and precedence rules
p = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.
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Re: Mathematics and precedence rules
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Re: Mathematics and precedence rules
Last edited by araveugnitsuga; 20121011 at 09:35 PM.
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Re: Mathematics and precedence rules
I only don't get the bit with X and T or whatever. The rest I could work out if I cared, or just recognise.
Error. Is that 48/(2*(9+3)) or (48/2)(9+3)?
=48/2(12) and now just left to right
=24(12)
=288 (all in my head, this is basic stuff)
WolframAlpha agrees with me, and so does my TI84.Jude P.
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Re: Mathematics and precedence rules
X is a matrix, transposing and inverting it and doing that on the reverse order are the same and give a null matrix.
The way WolframAlpha calculates implied multiplication is odd, as well as the TI series.
Implied multiplication in general is odd in terms of order of operations because it is considered above division and explicit multiplication.
It should be: 48/(2*(9+3))
Which gives off 2.Last edited by araveugnitsuga; 20121011 at 09:44 PM.
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Re: Mathematics and precedence rules
2, yes, but not on Windows 7
Ed: it ignores the 2 unless you add the extra parenthesis.Last edited by nedz; 20121011 at 09:52 PM.
p = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.
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Re: Mathematics and precedence rules
Jude P.
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Re: Mathematics and precedence rules
p = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.
Completely Dysfunctional Handbook
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Re: Mathematics and precedence rules
That's because you're entering the wrong formula. The correct one is 61*0+2/2=, not 61x0+2/2=.
Windows Calculator does not handle implied multiplication at all. So that other example is pointless. As above, you must enter the equation into the calculator in an accepted format, or it will not produce expected results.
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Re: Mathematics and precedence rules
When something is taught in elementary school, and then used in EVERY subsequent class in that field, it should be considered common knowledge. Just like you can assume that if you ask someone where you use a period or a question mark, they should know, because they've been doing it their entire life probably, and certainly their entire school career. People should know basic grammar and punctuation, and they should know the basic rules of math.
The main problem is that sadly, in the US (and probably other nations, but not having gone through their school systems, I can't make statements about them) math is taught in an absolutely horrid manner, and being proficient in math (or any subject, really) is seen as uncool by the majority of the youth. The over dependence on calculators (which are often wrong if you don't know how to use them, and most people don't) just complicates the problem, until you have the vast majority of the population essentially illiterate in math. (and nearly illiterate in English, but that's a different problem)
basically, it's not the equation's fault. it's either the students, for not caring enough to learn the main rule in all of math, or the teachers for not stressing it's importance or teaching it well enough.Avatar by Lycunadari
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Re: Mathematics and precedence rules
They are rather simple, much of them is intuitive except the products which are annoying to both operate and conceptualize.
Implied multiplication is above multiplication and division. The main argument is because its main use is alongside variables and constants.
So the idea is that 1/2x is not x/2 but 1/(2x). The T series and Wolfram Alpha consider it of higher precedence when no parenthesis is present between the implied multiplication terms, but disregard the priority when a parenthesis is involved in the conjoining.
Implied multiplication is an odd component of Order of Operations because it isn't used until much later, when in algebra, by that time the division sign is no longer in use due to the fact that writing fractions is infinitely more comfortable for working around with. The majority of authors give it higher precedence by citing the way it works with variables and constants.
In this case:
48/2q
Where q=9+3
So after replacement
48/(2*(9+3))
48/24
2Last edited by araveugnitsuga; 20121012 at 12:17 AM.
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Re: Mathematics and precedence rules
It would be much easier to just define X as a scalar. Since a scalar is a 1x1 matrix, the transpose of a scalar is itself, and the invert is just 1/itself. This gives us (0)! without needing a scalar transform on a matrix.
Coincidentally, I am curious what the X_bar is supposed to represent. We usually denote matrices with an uppercase letter or a bold letter, and I do not recall any operations that is denoted by a bar (other than mean, although that's a different field of math).

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Re: Mathematics and precedence rules
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Re: Mathematics and precedence rules
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p = 4
Consider a 5' radius blast: this affects 4 squares which have a circumference of 40' — Actually it's worse than that.
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Re: Mathematics and precedence rules
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Heh, haha, wow. No, they don't. Maybe where you live people can manage grammar, but hardly anybody around here knows even some of the pretty basic stuff. The subjunctive, who vs whom, &c.
Well, that's the idea of school, but...no.Jude P.
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