Question Number 149485 by abdurehime last updated on 05/Aug/21

proof that 1=2??

Answered by Olaf_Thorendsen last updated on 05/Aug/21

if A = B  A×A = A×B  A^2  = AB = BA  A^2 −B^2  = BA−B^2   (A+B)(A−B) = B(A−B)  A+B = B  2B = B  2 = 1

Commented bycherokeesay last updated on 05/Aug/21

  you can only simplify A−B on both sides of the equality (5th line) when A≠B !  but A = B ⇒ A − B = 0 !!!  so you will have 0 of the sides of this equality !

Commented bypeter frank last updated on 05/Aug/21

A+B=B  A=0

Commented byOlaf_Thorendsen last updated on 05/Aug/21

Of course sir !  But in the real life 1 ≠ 2 too.

Commented byMJS_new last updated on 06/Aug/21

I remember someone here proved  i=(√(−1))=±1  but I don′t remember how... that guy was  seriously convinced... as I stated before:  those who know nothing must believe everything

Commented byMJS_new last updated on 06/Aug/21

...on the other hand  f(x)=(x/x)  lim_(x→0) f(x) =1 ⇒ (0/0)=1  g(x)=((2x)/x)  lim_(x→0)  g(x) =2 ⇒ (0/0)=2    (0/0)=1∧(0/0)=2 ⇒ 1=2 q.e.d.    now what′s you argument Mr. Peter Frank?

Commented byMJS_new last updated on 06/Aug/21

๐Ÿคจ๐Ÿค”๐Ÿ™„๐Ÿคช

Commented byiloveisrael last updated on 06/Aug/21

the other way    lim_(x→0) ((sin x)/x)=1=(0/0)  lim_(x→0) ((tan (4x))/(2x))=2=(0/0)  then 1=2

Commented byOlaf_Thorendsen last updated on 06/Aug/21

1 = (√1)  1 = (√((−1)×(−1)))  1 = (√(−1))×(√(−1))  1 = i×i = i^2 = −1  1 = −1

Commented bymathmax by abdo last updated on 06/Aug/21

but its correct dans Z/2Z

Commented byMJS_new last updated on 06/Aug/21

many people (maybe most people) forget that  the rules in R are different from those in C.  (we usually don′t have to think about the  differences between the rules of N, Z and Q  as we just ♮walk throughε them while we  start to study)

Commented byajfour last updated on 06/Aug/21

2^(nd)  step to 3^(rd)   step is not  allowed, there are certain  rules here that need be  followed..

Commented bypeter frank last updated on 06/Aug/21

no argument sir.understood

Answered by puissant last updated on 06/Aug/21

a=b  ⇒ a^2 =ab  ⇒a^2 +b^2 =b^2 +ab  ⇒a^2 +b^2 −2ab=b^2 −ab  ⇒ 2a^2 −2ab = b^2 −ab car a=b  ⇒ 2a(a−b)=a(a−b)  ⇒ 2a=a soit 2=1...