I think you are overestimating either the number of people that would have any idea what -5^2 means or the percentage of people that would work it incorrectly.
Fantasy Football - Footballguys Forums
This is a sample guest message. Register a free account today to become a member! Once signed in, you'll be able to participate on this site by adding your own topics and posts, as well as connect with other members through your own private inbox!
Daughter's math homework (1 Viewer)
- Thread starter MrPack
- Start date
Smoo
Fear the Beaver
It didn't refute any claim that negative integers weren't self-contained units.Maurile did the best job of explaining how the "-" worked as an operator even in the case of its presence next to an integer, and roly provided the best framework for incorporating that explanation into a vector universe. Those two were the two who wooed me, everybody else was just fluff. Sorry.
Because "-" means "the opposite of". The opposite of -6 is 6.
bryhamm
Footballguy
Let me try one more time:(-5)^2 is "taking the value negative 5 and squaring it, which results in 25
while
-(5^2) is "taking the negative value of the answer to 5 squared, which is -25
I think everyone here agrees on the above two things.
In the absence of parentheses, -5^2 is the same thing that I wrote in my 2nd example. It is VERY poorly done and obviously causes confusion. That does not indicate that it is wrong.
I'll start by teaching 1 (you) and letting you pass the word along.
-(-6) goes in the opposite direction of (-6), which goes in the opposite direction of 6.So if 6 goes right, -6 goes left, and -(-6) goes right.
dgreen
Footballguy
Okay, so it is just a "directional" type thing like rolyaty was describing. I think I'm all clear on this. Glad I jumped in late and it didn't take me the full 20+ pages to get on board.
Edit to add: I just had a hard time grasping that direction would be a math proof, if that's what it is. I wanted to see a proof in numbers and wasn't seeing it.
Last edited by a moderator:
The Iguana
Footballguy
I want to know how the following isn't enough to prove it to anyone:-5^2 = 0 - 5^2 = -25
The Iguana
Footballguy
That just cracked me up!
How does it not?We start with the positive numbers. A negative is the opposite of a positive, so it is a number that has been modified.
Or maybe I don't understand what you mean by a "self-contained unit".
People who consider "-5" to be a self-contained number would see the above as an equivocation error.The "-" on the left-hand side of the equation doesn't mean the same thing as the "-" on the right-hand side of the equation. According to this view, the "-" on the right is an operator while the "-" on the left is part of a number.
rolyaTy
You're Heinous
Well, it's like with vectors, the solution to adding vectors comes from the resultant, and that is basically the shortest distance between the origin and the final point on a vector.Same thing with addition. You start at the origin, 0, and you follow the number line according to the equation. Math, in it's simplest form, is simply starting at the origin, and finding the total distance between where you started and where you end. The signs give you indication of the direction, and the values give you the units/displacement to travel.
To me, it makes the most sense to see + and - as directional cues as you travel over the number line.
Smoo
Fear the Beaver
Apparently not. My point was that the "-" in "-5" was not an operator but a character within the number, an indivisible part os the identity of said number. Your arguments didn't refute that, they all worked off of the initial assumption that the "-" was an operator, which was an assumption I was refusing to make.
The Iguana
Footballguy
What in the heck is a "self-contained number" suppose to be? Adding 0 to any equation does not change the equation, plain and simple. It is impossible for -5^2 <> 0-5^2 unless you change the fundamental theorems of math.
:IBTL:
He means that -5 is a combination of two characters representing a single value in the exact same way that 23 is.If you see 23^2, you treat 23 as a single value and square it (instead of just squaring the three before you do anything with the "2"); and along the same lines, if you see -5^2, you treat -5 as a single value and square it (instead of just squaring the five before you do anything with the "-").
Oh. It turns out that I do understand what you mean by a "self-contained unit". However, I have no idea of how to convince you to accept the fact that the "-" in "-5" is an operator. I would have similar difficulty in explaining why the numeral 3 in the number 538 is in the "tens" place rather than the "towns" place. I guess this is where I pull out my "just because" answer.
Last edited by a moderator:
The Iguana
Footballguy
Also, for this to be true:-5^2 <> 0 - 5^2
then this would have to be true:
-5^2 = 0 + (-5)^2
If the above were true then have changed the rules of order of operation and/or introduced the idea of "implied ()". I like to see someone try to create a set of rules that dictate the appropriate use of "implied ()".
RoarinSonoran
Footballguy
93 - 5^2 does not equal 93 + -5^2
You can't have two operators together. The proper way to write it is:
93 + (-5^2)
a - b <=> a + (-b)
Set a=93 and b=5^2 and you have
93 - 5^2
Thus,
93 + (-5^2) <=> 68 (since b=5^2=25)
Yes, going back to the original post, -5^2 is ambiguous. Remove the ambiguity with -(5^2) -- [or (-5)^2 if that's what you really intend the problem to be].
-5^2 <=> -25
Deal with it folks.
You can't have two operators together. The proper way to write it is:
93 + (-5^2)
a - b <=> a + (-b)
Set a=93 and b=5^2 and you have
93 - 5^2
Thus,
93 + (-5^2) <=> 68 (since b=5^2=25)
Yes, going back to the original post, -5^2 is ambiguous. Remove the ambiguity with -(5^2) -- [or (-5)^2 if that's what you really intend the problem to be].
-5^2 <=> -25
Deal with it folks.
The Iguana
Footballguy
wow. when I looked at this thread last night it was 5 pages long.
I'd enter this thread in the mathematics event of the FBG Special Olympics.
good one
Smoo, if someone looked at the number "538", said, "The 3 is in the towns place", and resisted all attempts to accept that it was in the tens place, how would you explain the correct answer to this person?"I don't know how to explain that" is good posting?
Smoo,Is 5 a self-contained number?
Last edited by a moderator:
Kleck
Footballguy
Look here, son. If you choose not to learn the basics and ground yourself in your beliefs, well, there's not much anyone else can do about that. Further, a bunch of high school and middle school math teachers is probably not the best place to research number theory. It all begins with the Natural numbers. I listed the hierarchy for you, but I don't think it sunk in.Naturals = 1,2,3,...
Whole = 0,1,2,3,...
Integers - ...-3,-2,-1,0,1,2,3,...
-5 is not a self contained number in the way you want to cling to. Its the opposite of 5. We write that as -5 as a short hand notation. Yes, we also use the - symbol for subtraction. Is it the best choice? Perhaps not if its going to cause so much confusion.
(HULK)
(Smash)
Can't we all agree that this equation:-5^2should never be used as it will cause confusion?Why be ambiguous when you can be clear by using (-5)^2 or -(5^2)?I understand that at some point, mathmaticians decided that-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable. For example -x^2 must equal -(x^2)... or else you get two possible values for x and that is undesirable. So, they made this decision.However, it enters into the realm of abiguity because negative five is expressed as -5 when it is standing alone. For this reason, plenty of people see -5^2 and assume the equation is saying negative five squared, not the opposite of five squared.Hence, its interpreted both ways by the general population. Someone somewhere down the line made the decision that one is accepted and the other is not to save time on using parenthesis. I call that intellectual laziness. I think the correct answer should've been to require parenthesis to make certain it was clear.
What is the opposite of 5?
RoarinSonoran
Footballguy
Aren't 0 and 8 the only self-contained numbers? The circles (ovals) make them wrap themselves up, all toasty and warm.
Then how can -5 be self-contained when it is nothing more than a modified 5?
I'd say yes.All complicated math expressions like 254^(45/2)+2*10^(-432) can ultimately be described as adding or subtracting the number one to itself a bunch of times (or fractions of times).
In that sense, 5 = 1+1+1+1+1.
Moreover, 25 = (2*10)+(5*1) = (1+1)(1+1+1+1+1+1+1+1+1+1)+(1+1+1+1+1) = (1+1)+(1+1)+(1+1)+(1+1)+(1+1)+(1+1)+(1+1)+(1+1)+(1+1)+(1+1)+(1+1+1+1+1).
In that sense, everything is an operation, and everything thereofre comes down to order of operations.
The first operation is to convert consecutive numerals into values by multiplying the last in the string by one, the second-to-last by ten, the third-to-last by a hundred, etc., and summing the respective products.
Once that's done, you apply operators such as ^, *, /, +, and -.
I would define "self-contained number" in Smoo's sense as any group of characters that are dealt with before any of the explicit operators.
So "5" is definitely a self-contained number in that sense.
Smoo was arguing that "-5" should also be a self-contained number in that sense (converting "-5" into the value of negative five before doing anything else with it, like squaring it).
By standard convention, though, "-5" is not a self-contained number in the Smoo sense because of fact the "-5" is not resolved into negative five before any operators are applied to it. The "5" is resolved into the value of five before any operators are applied, but then any "^" would take priority over the "-". Which means "-5" isn't self-contained.
But certainly "5" would be self-contained.
Last edited by a moderator:
cstu
Footballguy
My point is that, yes, a number can be negative. If it's labelled -5 then that means it's negative 5. If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between. Using a space is ridiculous for real world purposes so if it's meant to be an operator then () have to be used. Otherwise it's assumed to mean the number is negative. A lot of people seem to be over thinking this since if you were asked verbally what negative 2 squared is you would say 4. I think many of you are looking at it on the screen and making it seem more complex than it is.
Well duh.
Is 2 self-contained? Yes. What is 2+3? 5. Then how can 5 be self-contained when it is nothing more than a modified 2?
Because you and Smoo said it was.
