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Is the following the only reason why x ≠ ±x?by Turion
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#1
Sep313, 08:26 AM

P: 148

Assumption: x is unconditionally equal to ±x.
This makes sense because if you take a look at a graph of y=x, and plot any horizontal line y=C where C is some constant, you will always have two solutions: one is positive and one is negative. But if we substitute any number into x, then we realize that this actually contradicts: x = ±x Let x = 2 2 = ±2 2 = ±2 2 = 2 OR 2 = 2 Am I missing something or is the only reason why they aren't unconditionally equal? 


#2
Sep313, 08:32 AM

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That final statement is true, isn't it? So I don't see an issue there.
I think the problem you are running into is that "±x" isn't welldefined notation, whereas x is unambiguously defined. People often use it as shorthand, as you have done, for example in statements like "The solution of x² = 4 is x = ±2", but that is just an informal way of saying "The solutions of x² = 4 are x = 2 and x = +2". You could write "The solution of x² = 4 is x = 2" but that is technically something different  what you are saying then is: "The solutions to the equation x² = 4 are the same as the solutions to the equation x = 2" (and the solutions to both equations are x = 2 and x = 2). 


#3
Sep313, 08:35 AM

P: 25

the modulus of x equals x if x is nonnegative and x if x is less than zero. It does not equal ±x.
The equation mod(x)=2 has the solutions x= ± 2 


#4
Sep313, 08:49 AM

P: 148

Is the following the only reason why x ≠ ±x?
The issue is that you don't know if x is negative or nonnegative. 


#5
Sep313, 08:51 AM

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As I said, it is usually used as shorthand for "+2 or 2". 


#6
Sep313, 08:55 AM

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#7
Sep313, 04:23 PM

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#8
Sep413, 12:36 PM

P: 148




#9
Sep413, 12:46 PM

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#10
Sep413, 03:34 PM

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#11
Sep413, 06:30 PM

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#12
Sep513, 01:56 AM

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Can I give you some advice?
Actually, I'm going to do it anyway :P As long as you don't completely understand "±x", avoid using it. As I pointed out before, it does not have any formal definition like x does  it is merely used as shorthand. For the time being, I would suggest that you focus on getting the basics right. Writing "x = 2 V x = 2" is hardly more work than "x = ±2", it is unambiguous and it doesn't confuse anyone, including yourself. Once you have properly learned about functions and branch cuts you may be more sloppy :) 


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