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Posted

So I was reading some posts and saw rootbears sig and looked at it...and it does not work out.

 

a=1 b=1

a=b

a*a=a*b Multiply 'a' to both sides.

a^2=ab Simplify.

a^2-b^2=ab-b^2 Subtract 'b^2' from both sides.

(a+ B) (a- B) =b(a- B) Factor.

a+b=b Divide both sides by 'a-b'

1+1=1

2=1

 

When theoretically proving a math equation, you may always multiply both sides of the equation, now it must be both sides, with the exact same value, as done in line 3. But you may never add a value to the equation, because as you can see from the resultant it (can) return a value that is false, and cannot be. It is a basic rule of theoretical Mathematics.

 

Sorry just bugged me lol

Posted

However, you are absolutely wrong blum.gif

 

Adding/subtracting is perfectly fine. It is a basic rule of 3rd grade mathematics B)

 

The issue here is this:

Divide both sides by 'a-b'

 

This is valid only if a != b, which is not true. Therefore, it is invalid (division by zero).

 

Another way to look at it would be to view the operation as a function - you will see that as (a - b ) approaches 0 (as they approach equality), the value of the function approaches infinity (which happens in case of divide by zero).

 

The later part is basic calculus smile.gif

Posted
So I was reading some posts and saw rootbears sig and looked at it...and it does not work out.

 

a=1 b=1

a=b

a*a=a*b Multiply 'a' to both sides.

a^2=ab Simplify.

a^2-b^2=ab-b^2 Subtract 'b^2' from both sides.

(a+B )(a-B )=b(a-B ) Factor.

a+b=b Divide both sides by 'a-b'

1+1=1

2=1

 

When theoretically proving a math equation, you may always multiply both sides of the equation, now it must be both sides, with the exact same value, as done in line 3. But you may never add a value to an equation, because as you can see from the resultant it (can) return a value that is false, and cannot be. It is a basic rule of theoretical Mathematics.

 

Sorry just bugged me lol

 

actually, that's not the point. You CAN add/substract the same value on both sides of the equation.

if a = a, then a + b = a + b

 

The reason why this thing above is wrong is because you divide by 0 at some point.

When you divide both sides by ( a - b ) , you are actually dividing by 0 because a = b.

 

This proves that dividing by 0 makes no sense, mathematically speaking.

 

 

edit: SOS beat me to it...

Posted

Sorry for it being early, what I was trying to state was that adding something to both sides of an equation can not help you solve that equation.

 

And as for the division, the function, with predifined variables would be invalid, but the theory behind the equation would still be valid.

 

I was thinking two things and they got melded into one sentence.

Posted

It ("the theory" as you call it) would be invalid even without predefined parameters. It would be OK only for pre-highschool level problems where nobody cares about issues like this.

 

Why am I multiplied with NBV, Vile? blum.gif

Posted
you must make the rule, a!=b

which is in complete contradiction with the first statement of the "proof":

a=b

 

 

actually, a=1 and b=1 isn't needed to "prove" that 2=1

at then end you have:

a + b = b

b + b = b (because a = b )

2 = 1

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