RadiantPhoenix wrote:I think I might be able to do this one.Maxus wrote:He is also trying to prove that in algebra, and not 2e, -5=5.
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RadiantPhoenix wrote:I think I might be able to do this one.Maxus wrote:He is also trying to prove that in algebra, and not 2e, -5=5.
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Kaelik, to Tzor wrote: And you aren't shot in the face?
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Just a heads up... Your post is pregnant... When you miss that many periods it's just a given.
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to anyone understanding order of operands it does NOT look reasonable, because braces and parenthesis are done before multiplication and division.Josh_Kablack wrote:it was something like expanding (a - b) ^2 to ( a^2 - b^2 ) which looks reasonable at a glance, despite being incorrect.
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Code: Select all
2.24i 2.24
----- = -----
2.24 2.24i or i = 1/i
Kaelik, to Tzor wrote: And you aren't shot in the face?
Frank Trollman wrote:A government is also immortal ...On the plus side, once the United Kingdom is no longer united, the United States of America will be the oldest country in the world. USA!
Actually, no.fectin wrote:-1 is a number, not an operation. Order of operations is inapplicable.
Claiming that -1^2 = -1 is like claiming 12^2 = 14.
Kaelik, to Tzor wrote: And you aren't shot in the face?
Frank Trollman wrote:A government is also immortal ...On the plus side, once the United Kingdom is no longer united, the United States of America will be the oldest country in the world. USA!
You are mistaken. That's just distributing exponentiation over multiplication:Doom wrote:Between steps 3 and 4 is wrong because you can't use square root properties ("square root of a ratio is a ratio of square roots") when an argument is negative.
First of all, the same order of operations is not observed in all contexts. For example, mathematicians usually give multiplication higher precedence than division, but in computer programming they are usually given equal precedence and simply read left-to-right. So an expression like "6 / 3 * 2" actually has a different answer depending upon which set of rules you use.Josh Kablack wrote:-1^2 == -1
Because if you strictly follow order of operations, exponentiation is performed before multiplication, even multiplication by a negative coefficient.
Uh, no.Manxome wrote:You are mistaken. That's just distributing exponentiation over multiplication:
(a*b)^c = a^c * b^c
That's a completely general rule, and is true even when a is negative and c = 1/2.
Wikipedia wrote: Because of the discontinuous nature of the square root function in the complex plane, the law √zw = √z√w is in general not true.
And the very next step is the mistake. "The square root of a product is a product of square roots", only applies if the arguments are positive; much as in your 'general rule' above, it doesn't work if both arguments are negative.Here's an alternate version I saw in college that requires no division:
1
= sqrt[ 1 ]
= sqrt[ (-1)*(-1) ]
Well, it has one answer according the proper rules. There is only one order of operations. Honest, mathematicians give multiplication the same precedence as division, reading left to right (again, go and pick up an algebra textbook and see for yourself). Every mathematician will give the same value to that calculation, 4. Every. Single. One. There is only one answer, as per order of operations.First of all, the same order of operations is not observed in all contexts. For example, mathematicians usually give multiplication higher precedence than division, but in computer programming they are usually given equal precedence and simply read left-to-right. So an expression like "6 / 3 * 2" actually has a different answer depending upon which set of rules you use.
And, yes, in formal notation, "-1" means "the additive inverse of 1". When a mathematician writes " 5 - 1", what he formally means is "5 + (-1)", honest.But more importantly, that is not a multiplication in any notational scheme I have ever heard of. I believe most mathematicians would simply say that "-1" is a number, but in computer land we would say that that is the number "1" preceded by the unary negation operator.
Kaelik, to Tzor wrote: And you aren't shot in the face?
Frank Trollman wrote:A government is also immortal ...On the plus side, once the United Kingdom is no longer united, the United States of America will be the oldest country in the world. USA!
OK, you are discussing principal roots and I am discussing general roots. I'm sure there exists some restricted set of transformations that are allowed on principal root operations that preserve equality, but I can't recall ever learning or needing to know exactly what that set is, despite taking math classes up through differential equations and multivariable calculus.Doom wrote:Uh, no.
Try a = -1, b = -1, and c = 1/2, and see for yourself it doesn't hold as a "general" rule. Honest, go and look in an algebra textbook, it specifically says you can't use certain radical properties if the arguments are negative. It is exactly because square root means the principal root (i.e., the positive root), that you cannot use radical properties for negative numbers.
I, and at least 3 other people I talked to when determining the grammar for a parser I was writing, were all taught in school that multiplication binds tighter than division.Doom wrote:Well, it has one answer according the proper rules. There is only one order of operations. Honest, mathematicians give multiplication the same precedence as division, reading left to right (again, go and pick up an algebra textbook and see for yourself). Every mathematician will give the same value to that calculation, 4. Every. Single. One. There is only one answer, as per order of operations.
I'm discussing 'square root' as it means in the context of the original proof, and nothing else. There's not much I can do but again ask you to look it up in a textbook if you just don't believe me. You might have gotten away with not knowing the difference in the classes you've taken, but I teach it that way in every math class, up through differential equations and multivariable calculus, and complex analysis, for that manner.Manxome wrote:OK, you are discussing principal roots and I am discussing general roots...but I can't recall ever learning or needing to know exactly what that set is, despite taking math classes up through differential equations and multivariable calculus.
Again, consult a mathematics textbook and see with your own eyes if you don't believe me. I just don't know what else to tell you. Division means "multiply by the reciprocal", it's just multiplication by a different name, it simply doesn't make sense to claim that multiplication 'binds tighter' than multiplication.I, and at least 3 other people I talked to when determining the grammar for a parser I was writing, were all taught in school that multiplication binds tighter than division.
As a slash, yes, a/bc is read as (a/b)*c (note how I use parenthesis to be perfectly clear, rather than use ambiguous spacing). There's an important 'special rule' that distinguishes between division with a slash, and a straight line.If you're reading a math textbook as you see the expression "a / bc", you would interpret that as "(a/b)*c"?
Kaelik, to Tzor wrote: And you aren't shot in the face?
Frank Trollman wrote:A government is also immortal ...On the plus side, once the United Kingdom is no longer united, the United States of America will be the oldest country in the world. USA!
Sorry. I was also discussing "square root" as it means in the context of the original proof, but I was under the impression that a radical meant "square root" and that you put a sign in front of it if you wanted only one of the roots, so that the notation used in the original proof referred to square roots. Wikipedia apparently disagrees with this usage, claiming that a radical always and only means the principal root. I apologize for the confusion.Doom wrote:I'm discussing 'square root' as it means in the context of the original proof, and nothing else.
It would go a long way, if you had actually done that. But I was most emphatically clear that I believed it applied to square roots (as in, the inverse of the square function) and NOT to principal square roots, and your example (a = -1, b = -1, c = 1/2) does not constitute a counter-example in that context:Doom wrote:Keep in mind, I've already shown your 'general rule' to be false in a specific case, which should go a long way to suggesting your general rule is not, in fact, general.
Yes.Doom wrote:there's a caveat that a straight line in this context is interpreted as including parenthesis for whatever is above, and below, the straight line.
Yes.Doom wrote:it's understood that anything in the radical is implied to be in parenthesis, even though such parenthesis are seldom written.
Absolute value involves putting symbols on both sides of the expression it's applied to, I can't think of anything else it could even theoretically mean. How would you even evaluate |a-b| if that were not true?Doom wrote:|a- b| really means |(a-b)|
But I am utterly surprised by this one. I would have bet money that you would agree that was a/(b*c).Doom wrote:yes, a/bc is read as (a/b)*c
I thought it was fairly obvious that I was using ambiguous spacing specifically so that I could ask you how you'd interpret the ambiguity. I thought that was a fairly reasonable way to use it.Doom wrote:note how I use parenthesis to be perfectly clear, rather than use ambiguous spacing
And here you're just being deliberately obtuse. This makes exactly as much sense as claiming that multiplication is just looped addition so multiplication and addition can't possibly have different precedence.Doom wrote:Division means "multiply by the reciprocal", it's just multiplication by a different name, it simply doesn't make sense to claim that multiplication 'binds tighter' than multiplication.
Not, not just Wikipedia, but every single mathematics textbook defines the radical in that fashion. It's a definition, Wikipedia 'disagrees' with your usage because your usage violates the definition, and is thus wrong. Doyou have a calculator? If so, press the radical (for square root) of, say, 9, and see if the answer is "3" or "+/- 3". The reason why your calculator says 3 is because it's using the same definition for radical (and note, "radical", as opposed to "square root") as everyone else but, apparently, you.Manxome wrote:
Wikipedia apparently disagrees with this usage, claiming that a radical always and only means the principal root.
Yes, if you take squre root to mean something besides what it actually means, there is no contradiction, but generally, making up your own meanings for words is bad form, particularly in mathematics. Square root (in this context, as a radical) has a particular definition, as per Wikipedia and every single mathematics textbook...you can't change the definition to something else at a whim.square roots (as in, the inverse of the square function) and NOT to principal square roots, and your example (a = -1, b = -1, c = 1/2) does not constitute a counter-example in that context:
sqrt[ (-1)*(-1) ] = +/- 1
sqrt(-1) * sqrt(-1) = (+/- i)*(+/- i) = +/- 1
No contradiction that I can see.
Again, I will reference every single mathematics textbook ever written. There's just not much more I can do about it...division is defined as the inverse of multiplication, and generally is done by multiplying by the reciprocal (note the reciprocal is the multiplicative inverse of a number), so it has the same precedence as multiplication.And here you're just being deliberately obtuse. This makes exactly as much sense as claiming that multiplication is just looped addition so multiplication and addition can't possibly have different precedence.
I was trying to help by quoting the most basic definitions, I'm sorry if the basic definitions look stupid to you. Again, please consult a basic math textbook and read it with your own eyes...I just don't know what else to tell you.The least stupid way I can possibly read your statement here is as meaning that you would personally find it counter-intuitive if the / and * operators had different precedence, which is at best tangential to the discussion.
Kaelik, to Tzor wrote: And you aren't shot in the face?
Frank Trollman wrote:A government is also immortal ...On the plus side, once the United Kingdom is no longer united, the United States of America will be the oldest country in the world. USA!
you just gave an example...fectin wrote:Could someone give me an example where order of operations makes a difference between multiplication and division, or between addition and subtraction? I'm pretty sure you can evaluate them however you want, as long as you get innermost parentheticals first, exponents next
Swordslinger wrote:Or fuck it... I'm just going to get weapon specialization in my cock and whip people to death with it. Given all the enemies are total pussies, it seems like the appropriate thing to do.
Lewis Black wrote:If the people of New Zealand want to be part of our world, I believe they should hop off their islands, and push 'em closer.
No, they're not the same thing. I know citing references doesn't do any good in this forum, but I'll mention that "Elementary Algebra for College Students" (Angel, 7th edition), notes on page 70 thatsabs wrote:Firstly
-1^2 and (-1)^2 are the exact same mathematical statement.
Kaelik, to Tzor wrote: And you aren't shot in the face?
Frank Trollman wrote:A government is also immortal ...On the plus side, once the United Kingdom is no longer united, the United States of America will be the oldest country in the world. USA!