Why 1=2... (1 Viewer)

[Kmahal1990]

Let A be numerically equal to B, and A = 1.

A=B
AB=B^2
AB-A^2=B^2-A^2
A(B-A)=(B-A)(B+A)
A=A+B
Sub A=1,B=1
1=2

Or
A-A=B
B=0
B= 1
1=0

What went wrong there? :S

 

[pLuvia]

Well from this line
(A+B)^2 - 2AB=B(A+B)
to this line
A+B-2AB=B
How did you cancel out the (A+B) from both sides?

There's your problem

 

[Bank$]

Well from this line
(A+B)^2 - 2AB=B(A+B)
to this line
A+B-2AB=B
How did you cancel out the (A+B) from both sides?

There's your problem

yeah u cannot do that cause u should have 2AB/(A+B)

 

[drynxz]

A(B-A)=(B-A)(B+A)
A=A+B

those two lines...if b=a then b-a will equal 0...u cannot divide through zero.

 

[victorheaven]

u said A=B
how can u divide both sides by A-B?
two sides are identically equal..

 

[morganforrest]

A(B-A)=(B-A)(B+A)
A=A+B

those two lines...if b=a then b-a will equal 0...u cannot divide through zero.

This is the correct answer as if A=B=1 then A - B = 0 and you can't divide by zero or Euler or someone will come and kick ur dog for being a dumbass....

QED

 

[SeDaTeD]

Or he could be working over the ring containing just {0}.

 

[Slidey]

Sigh.

 

[Scooter89]

yeah you cant divide by zero. consider another simplistic method with the same fault:

X^2 - X^2 = X^2 - X^2

therefore X(X-X) = (X+X)(X-X)

dividing by (X-x), ie dividing by zero, we have..


X = X + X

dividing by X, we have

1 = 1 + 1

ie

1 = 2... see?

 

[tommykins]

These are always fail.

 

[Slidey]

pLuvia should make a sticky thread about why 1 doesn't equal 0 lol

Here's a question: Is it possible that if AB=0, neither A nor B = 0? If not in normal algebra, is there an algebra in which it is possible?

 

[LoneShadow]

pLuvia should make a sticky thread about why 1 doesn't equal 0 lol

Here's a question: Is it possible that if AB=0, neither A nor B = 0? If not in normal algebra, is there an algebra in which it is possible?

Any ring which is not an integral domain will have that property. Called zero devisors. for example consider the ring of integers modulo 4: 2*2 = 4 = 0 ; but 2 is not zero.

...it basically depends on the how you define your operations. For all I care you could define the multiplication to be trivial: i.e. a*b = 0 for all a,b.

P.S. Don't confuse high school kids with ring theory Robert