Thorn
Footballguy
Actually the more I think about it, it should be a worldwide association.
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Daughter's math homework (1 Viewer)
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The Iguana
Footballguy
-5^2 is acceptable... it's sloppy but it is acceptable.This is an acceptable equation
^2 - 15x + 25 = -5^2 there are a number of ways to solve it, one of which is:1. add 5^2 to both sides^2 - 15x + 25 + 5^2 = -5^2 + 5^2equates to^2 - 15x + 25 + 25 = 0from there you eventuall get that x = 5 or x = 10if you even think of trying to say that you have to subract (-5)^2 from both sides of this equation, you have no mathematical case or presidence to stand on.
bostonfred
Footballguy
-5^2 + 5^2 = 50. I guess that might "eventuall" help us solve the problem, but it seems like the scenic route to get there.-5^2 is acceptable... it's sloppy but it is acceptable.This is an acceptable equation
bostonfred
Footballguy
Maybe on the scenic route we can eventuall see the presidence on Mt. Rushmore.
dparker713
Footballguy
I used "written as" and not "equals" for a specific reason. We're discussing notation. So yes, "written as" is appropriate. I'm not describing their mathematical equivalence, I'm describing their notational equivalence. Just as the 3 spatial coordinates can be written as x, y, z or as x1, x2, x3 - I am NOT saying that x=x1, just that both notations are valid provided they are both applied and interpreted consistently. I am also not agreeing the -5^2 = 25, just that it could be either. I do generally see that particular notation as the square of a negative integer, but I'd never use such sloppy notation.
I don't think so.The symbols we use, and the rules we have for manipulating them, are matters of convention. But the underlying math is, I think, objectively real. Integers exist as mathematical objects apart from our ability to conceive of them, and 2 + 2 = 4 would be a fundamental mathematical truth even if it tended to be false as a matter of physics. (Meaning that, in an alternate universe, whenever we took two apples and put them next to another two apples, if we somehow ended up with three apples, or five, because of some screwy alternate law of physics, it wouldn't change the fact that the integer two, when added to itself, would make four. In our universe, physics and math seem completely aligned — and indeed a universe in which physics and math are aligned may be the only type of universe that can possibly exist. But even if that weren't the case, I think math is real in and of itself; it doesn't depend on any agreement from physics to be real.)
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bostonfred
Footballguy
-5 is not notatioally equivalent to -1*5. It is notationally equivalent to (-5). It is mathematically equivalent to (-1*5).
Jayrod
Footballguy
That's a lot of words stuffed into the parenthesis.
That's still the rule.But in the expression -5^2, the base of the exponent is a positive number (5) and the exponent is a positive number; so the resulting value will be positive.Then after you get a positive number resulting value from the exponentiation, you apply the minus sign out in front, and the resulting value for the overall expression is negative.LarryAllen said:
dparker713
Footballguy
I find it amazing that your bias is so ingrained that you utterly fail to recognize it.-5^2 would only be acceptable for personal notes, and then only if you were consistent. It's unacceptable notation to present as an answer or to another person because it is ambiguous - an ambiguity that can easily be fixed. And the equation you presented is just as equally valid to be x^2 - 15x = 0 as it is to be x^2 - 15x + 50 = 0.-5^2 is acceptable... it's sloppy but it is acceptable.This is an acceptable equation
Impressed?
bostonfred
Footballguy
Flozhuwig * Malowkanjx = Galonkowicz. This is universally true. It doesn't depend on any agreement from physics to be true. In fact, we have not seen a physical instance of Galonkowicz in the known universe. But it's an undeniable mathematical truth. It's usually more meaningful to us to use examples that have meaning in our physical universe. It's certainly easier to prove their mathematical correctness of concepts we can understand. But there's no sense in arguing the value of Galonkowicz. It's a universal truth.
dparker713
Footballguy
Thats entirely dependent upon which computer program you're using.
"Written as" is a synonym for "expressed as."For any given number, there are numerous way to express it. Negative five can be expressed as "-5" or "(-1)*5" or any other number of ways.
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Jayrod
Footballguy
Definitely. I'd never have the audacity to attempt such a maneuver, yet you do it with such nonchalance...it's striking really.
Right, because some programs use the standard convention while others use a non-standard convention.I can whip up a program in a few minutes that, when you ask it what "2 + 2" equals, would return a value of "5". That doesn't make it right (in the sense of following the standard convention).
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bostonfred
Footballguy
Fixed to make your description less contentious. I think both sides will agree with the statement above as written.Now let's set x equal to five. I agree with you still that -x^2 = -25, because if we replace x with (5), we get -(5)^2 = -25Now let's look at a different notation: x^2. If you replace (x) with (-5), I no longer agree with you that (-5)^2 = -25The question is clearly where the parentheses go. The parentheses in -x do not go around the minus sign (-x). They go around the x. x is notationally equivalent to (x) and is mathematically to 1(x). -x is not notationally equivalent to (-x). It is notationally equivalent to -(x), which is mathematicallly equivalent to -1(x). On the other hand, -5 is notationally equivalent to (-5). Which is why (-5)^2 is equal to 25, not -25.
Bronco Billy is conceptually correct here. He just forgot to put parentheses around the -1.Bronco Billy said:
Psychopav
Help us, Joebi-Wan Brynobi, you're our only ho
I graduated high school in '89 and think you're on crack. So if it changed, it had to happen somewhere between '82 and '89. I learned how to teach math in '90 - '93, and it never came up. Just sayin'...
You didn't make it less contentious, because my post wasn't contentious in the first place. By substituting x for 5, you just made it less specific.
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Psychopav
Help us, Joebi-Wan Brynobi, you're our only ho
FYPThe Iguana said:You are wrong. That is all.Thorn said:I just believe -5 is a number, not an operation on another number, that's all.
The convention is arbitrary, and apparently not universally taught recalled. I fail to see how anyone can be flatly wrong in this discussion.Psychopav said:I believe purple is a number.I also believe the government is out to get me.Thorn said:I just believe -5 is a number, not an operation on another number, that's all.
Thorn
Footballguy
Is that forgetfulness an indictment of private education?
Come on, man. You should know that I never contended that (-5)^2 = -25.Why make it look like I did?
Jayrod
Footballguy
-5^2 = 25Seriously, 29 pages on this?-5^2 = -25
Psychopav
Help us, Joebi-Wan Brynobi, you're our only ho
But didn't you just say that what 2 + 2 equals is objective mathematical truth, not following a convention?
Ilov80s
Footballguy
Nope, put it into a scientific calculator and you will see you are wrong.-5^2 = 25Seriously, 29 pages on this?
Chaka
Footballguy
Wait. Wait. I think I can explain this whole thing. Marklar, these marklars want to change your marklar. They don't want Marklar or any of these marklars to live here because it's bad for their marklar. They use Marklar to try and force marklars to believe they're marklar. If you let them stay here, they will build marklars and marklars. They will take all your marklars and replace them with Marklar. These marklar have no good marklar to live on Marklar, so they must come here to Marklar. Please, let these marklars stay where they can grow and prosper without any marklars, marklars, eh or marklars.
Jayrod
Footballguy
Excel says it is 25. More people use Excel for calculations everyday than use a scientific calculator in a year. Since we are talking about a language, it is the translation of that language that is generally understood by the people who speak the language that matters.Microsoft and I say 25.Nope, put it into a scientific calculator and you will see you are wrong.-5^2 = 25Seriously, 29 pages on this?
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Jayrod
Footballguy
I don't know what this is from, but I laughed.
I put quotes around the 5 for a reason. Using the symbol "4" to express the value of four (i.e., the first positive counting number added to itself three more times) is a matter of convention. Other cultures have used different symbols (e.g., "IV"). My program might use "5". So it could get the actual math right, but return a value that appears to be wrong because it uses a non-standard convention. Like Excel does with -5^2.
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bostonfred
Footballguy
-5 cannot be expressed as (-1)*5. It is mathematically equivalent to -1*5, which is almost synonymous. But it's not notationally equivalent. -5 is notationally equivalent to (-5). (-1)*5 is notationally equivalent to (-1)(5) and to (-1)*(5). (-1)*5 is NOT notationally equivalent to -5, but it IS mathematically equivalent. As such, you can replace (-5) with its mathematical equivalent (-1*5). That's really the fundamental distinction in this argument. It's a necessary distinction, too. If we extrapolate your assumption that they are notationally equivalent, and thus that -5 can be replaced with it's "notational equivalent" of (-1) * 5, then it must also be similarly replacable by 0-5 and 17-22. And if we express -5^2 as 0-5^2, we do get -25. But if we replace -5^2 with 17-22^2, we do not get -25. We get a totally different number. If you want to replace -5 with 0-5, or with -1*5, or 17-22, you MUST use parentheses to notate their MATHEMATICAL equivalence. Let's try it again:(0-5)^2 = 25(-1*5)^2 = 25(17-22)^2 = 25All of those statements work because we are replacing things properly. But while -5 is not the notational equivalent of (-1)*(5), -x^2 is different. -x is the notational equivalent of -1x which is the notational equivalent of (-1)*(x). Those are all precisely identical due to the language with which we describe variables. Why are these different things? Simply stated, because -x is a shorthand way of saying -1x. -5 is not a shorthand way of saying -15.
bostonfred
Footballguy
I kept the correct part. I thought you'd appreciate that.
I'm not sure whom you're arguing with here. Has anybody contended that -5 is a shorthand way of saying -15? If you think the answer is yes, I suspect you are misunderstanding people's arguments.
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Ignoratio Elenchi
Footballguy
I am confident that if you sent this:
-52 = ______
to every math professor in the world, just about all of them would fill in that blank with -25.
Did that have to be the convention that everyone would agree on? No. You could make a perfectly good case that we should treat that as (-5)2 instead. But we don't.
Now, talking about how calculators and other computer programs handle it is a completely different (and not entirely relevant) question. They have their own conventions about how things are entered. If I type [negative] [5] [^] [2] in my calculator (at least the one I have here), it returns 25. That may or may not be correct. It depends entirely on whether or not I entered it correctly. By pressing the keys in that order, I explicitly told the calculator that I wanted to square the integer -5. If that's not what I wanted, then I needed to enter those commands in a different order.
But when one human writes -52 on a piece of paper, the convention humans have adopted when simplifying that by hand is to apply the exponentiation before the negation. -52 = -25. If that's not what I wanted, then I need to write the expression in a different way, to make it explicitly clear that I want to square the integer -5.
-52 = ______
to every math professor in the world, just about all of them would fill in that blank with -25.
Did that have to be the convention that everyone would agree on? No. You could make a perfectly good case that we should treat that as (-5)2 instead. But we don't.
Now, talking about how calculators and other computer programs handle it is a completely different (and not entirely relevant) question. They have their own conventions about how things are entered. If I type [negative] [5] [^] [2] in my calculator (at least the one I have here), it returns 25. That may or may not be correct. It depends entirely on whether or not I entered it correctly. By pressing the keys in that order, I explicitly told the calculator that I wanted to square the integer -5. If that's not what I wanted, then I needed to enter those commands in a different order.
But when one human writes -52 on a piece of paper, the convention humans have adopted when simplifying that by hand is to apply the exponentiation before the negation. -52 = -25. If that's not what I wanted, then I need to write the expression in a different way, to make it explicitly clear that I want to square the integer -5.
Ilov80s
Footballguy
You can't trust Fred. He turned the Don/Dawn debate into a mess.
Ignoratio Elenchi
Footballguy
5^2 - 5^2 = 400.
Thorn
Footballguy
Of course not.
bostonfred
Footballguy
My contention is as follows:If x = 5, -x^2 = -25. However, -5^2 =25, NOT -25.If this is true, then the burden on me is to prove why -x is distinct from -5 if they both have a minus in front of them. I am doing so by showing that -x and -5 are different in the same way that 2x and 25 are different and -1x and -1x are different. The minus sign has a different meaning when placed in front of a variable than when placed in front of a number. A minus sign in front of a number is an adjective. It's a way of describing a complete concept. A minus sign in front of a variable is an operation. It's a way of describing the number by which we multiply the variable. I fully agree with you that nobody is contending that -5 is a shorthand way of saying -15. Yet you specifically have argued that -5 is the notational equivalent of saying -1*5. That is not true. It's the mathematical equivalent, not the notational equivalent. As such, you may replace -5 with (-1*5) or even ((-1)*(5)) if you prefer. But you can't replace it without using parentheses around it, anymore than you can replace it with 17-22 without using parentheses.
rodg12
Footballguy
I am confident that if you sent this:
-52 = ______
to every math professor in the world, just about all of them would fill in that blank with -25.
Did that have to be the convention that everyone would agree on? No. You could make a perfectly good case that we should treat that as (-5)2 instead. But we don't.
Now, talking about how calculators and other computer programs handle it is a completely different (and not entirely relevant) question. They have their own conventions about how things are entered. If I type [negative] [5] [^] [2] in my calculator (at least the one I have here), it returns 25. That may or may not be correct. It depends entirely on whether or not I entered it correctly. By pressing the keys in that order, I explicitly told the calculator that I wanted to square the integer -5. If that's not what I wanted, then I needed to enter those commands in a different order.
But when one human writes -52 on a piece of paper, the convention humans have adopted when simplifying that by hand is to apply the exponentiation before the negation. -52 = -25. If that's not what I wanted, then I need to write the expression in a different way, to make it explicitly clear that I want to square the integer -5.
TRUTH.
Ignoratio Elenchi
Footballguy
5^2 - 5^2 = 0.000064
Ignoratio Elenchi
Footballguy
5^2 - 5^2 = 1,953,125
They're pronounced the same.The thing is, I think bostonfred already stated a few pages ago (unless I'm remembering wrong) that -5^2 = -25 according to what the convention actually is. He just thinks that -5^2 = 25 under what the convention should be, if the convention were to make more sense. That's similar to the view Smoo undertook.
That's fine. People can reasonably disagree about what the convention should be. There may be decent arguments on both sides.
But the question of what the standard convention actually is appears to be definitively settled. So I don't know why people (including bostonfred, unless I'm misreading his most recent posts) are continuing to discuss that question.
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Ilov80s
Footballguy
If -5^2 is equal to a positive 25, than 5^2 -5^2 would simplify to 25+25. However, 5^2 - 5^2 simplifies to 25 - 25.
rodg12
Footballguy
By their line of thinking, they'd be more likely to think it's 625. They read -5^2 as (-5)^2 so 5^2-5^2 = 5^2((-5)^2).
Hooper31
Footballguy
To say there is "clearly" not a universally accepted convention is just wrong. This is akin to a person standing outside on a sunny day pointing at the sky claiming that is actually raining constitutes enough of an opposition to argue against a universal convention of what precipitation means.If you put 1000 random high school and college mathematics professors in a room you're going to find a few of them that will argue that there is some ambiguity while the other 990+ just sort of roll their eyes into their heads wondering why anyone would bother wasting time with the argument.
There are many national and worldwide associations of mathematicians. Currently I belong to the NCTM and I routinely participate in the forums at Drexel University. One of the popular forums there is Ask Dr. Math. This same discussion has taken place many times. Yes, there are a few holdouts that argue against the convention just like you will find in any other arena, but the reality is that the overwhelming majority of professionals in the mathematics field agree on the convention.
Thorn
Footballguy
You don't have any -5's in your original example. It would simplify to 25 - 25. I like how you tried to sneak the negative sign right up against the 5 there without a space in your second post to make it confusing. Nice try.
Bronco Billy
Footballguy
Cheese and crackers.
If a discussion comes up about fractions, Joe is going to have to open a new website.
Fractionguys.com®
If a discussion comes up about fractions, Joe is going to have to open a new website.
Fractionguys.com®
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