- #1

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if X= the square root of 1

the square root of 1 = 1 or -1

the square root of 1 = the square root of 1 these are true yes?

therefore 1 = -1

X-X = 2 because 1--1=2

X-X = -2 because -1-1=2

X-X = 0 because 1-1=0

- Thread starter chalky00
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- #1

- 20

- 0

if X= the square root of 1

the square root of 1 = 1 or -1

the square root of 1 = the square root of 1 these are true yes?

therefore 1 = -1

X-X = 2 because 1--1=2

X-X = -2 because -1-1=2

X-X = 0 because 1-1=0

- #2

DaveC426913

Gold Member

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You cannot conclude that 1 = -1 from your initial arguments. It does not follow.i have been wondering about something and i can think of a way to prove myself wrong so... here it is:

if X= the square root of 1

the square root of 1 = 1 or -1

the square root of 1 = the square root of 1 these are true yes?

therefore 1 = -1

- #3

arildno

Science Advisor

Homework Helper

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Suppose you have the equation:

[tex]x^{2}=1[/tex]

This can be rewritten as:

[tex](x-1)*(x+1)=0[/tex]

and x can then either be 1 or -1.

It does not follow that

1=-1

- #4

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X=X

the square root of 1 = the square root of 1

the square root of 1 = 1

the square root of 1 = -1

therefore x can be 1 or -1

therefore x-x=2 or -2 or 0 im trying to find an explanation as to why its wrong.. i know its wrong but i dont know why... it seems logical and illogical at the same time

- #5

DaveC426913

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X can be 1

Walk it through.

root(x) can be 1 or -1.

- #6

JasonRox

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Above!

[tex]x^{2}=1[/tex]

This can be rewritten as:

[tex](x-1)*(x+1)=0[/tex]

and x can then either be 1 or -1.

It does not follow that

1=-1

- #7

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your not explaining your telling, sorry for not taking your word as gospel but feckin prove it

- #8

DaveC426913

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Are you seriously copping a 'tude?your not explaining your telling, sorry for not taking your word as gospel but feckin prove it

Ths onus is on you to lay down math that is valid. It is not valid.

The fact that you don't follow it does not give you cause to be rude.

I'll try again.

X can be 1 or -1.

That's an

When you write your equation x-x=0

and then substitute for x, you write (1)-(-1)=0. You cannot do this.

- #9

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i just want an explanation ... it doesnt make sense and im sorry ive been thinking about it for ages and you just say no with no evidence

- #10

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why cant they be used independently?

- #11

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surely 1 equation cant give 2 answers

X must have 2 values in this case?

- #12

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Your equation is x

Case 1: x=1; does this satisfy the equation? Yes, 1

Case 2: x=-1; does this satisfy the equation? Yes, (-1)

The two cases do not overlap, one is true or the other one is true, if you consider the original equation with x being 1 sometimes and -1 at other times, perhaps (x)(x)=(1)(-1)=-1 and this doesn't satisfy the equation.

Of course an equation can give two answers, an equation can give as many answers as there are numbers.surely 1 equation cant give 2 answers

X must have 2 values in this case?

- #13

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hmm im still not convinced

- #14

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Then you need to meditate on it, because I don't think any more explanation will help.

- #15

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when you say

Of course an equation can give two answers, an equation can give as many answers as there are numbers.

what do you mean? 1+1 = 2 and only 2?

2+2=2 and only 2

the square root of one equals 1 and -1

- #16

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X = the square root of 1 theres your overlap

- #17

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I mean exactly what I say. Your equation is a perfect example. x

- #18

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if theres an infinite number of values then doesnt that basically mean its meaningless? actually dont explain that i learn too slow... look im sorry i just dont understand why there is no overlap but its fine i can live with it... cheers tho anyway

- #19

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It is not meaningless, its meaning is that x=nPi where n is any integer.

- #20

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haha i get it... ok thanks very much... sorry for being a bit dense ha cheers

- #21

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ahh i ve lost it again

- #22

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haha joke...

x=nPi that has a variable though ... x= tsro1 doesnt

- #23

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tsro=the square root of btw

- #24

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Square root of a number is positive as defined by the principle root. (Square root of 1) =/= -1...However, functionally, X

if X= the square root of 1

the square root of 1 = 1 or -1

the square root of 1 = the square root of 1 these are true yes?

therefore 1 = -1

X-X = 2 because 1--1=2

X-X = -2 because -1-1=2

X-X = 0 because 1-1=0

One way that

You can also refer to this statement:

...exponentiation is not a function; it's what is sometimes called a "multi-valued function": to each input value, there can be more than one output values.

Last edited:

- #25

DaveC426913

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Just use 'root'. It has the same number of letters and has the advantage of not having to be explained.tsro=the square root of btw

The error you're making is thinking that the square root of 1 is 1 and -1.

This is not true.

The square root of 1 is 1

X is 1

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