proof-that-1-2-

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 \times A = A \times B

A^{2} = AB = BA

A^{2} - B^{2} = BA - B^{2}

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

A + B = B

2 B = B

2 = 1

Commented by cherokeesay last updated on 05/Aug/21

you can only simplify A - B on b o t h s i d e s o f t h e e q u a l i t y (5 t h l i n e) w h e n A \neq B!

b u t A = B \Rightarrow A - B = 0!!!

s o y o u w i l l h a v e 0 o f t h e s i d e s o f t h i s e q u a l i t y!

Commented by peter frank last updated on 05/Aug/21

A + B = B

A = 0

Commented by Olaf_Thorendsen last updated on 05/Aug/21

Of course sir!

But in the real life 1 \neq 2 too .

Commented by MJS_new last updated on 06/Aug/21

I remember someone here proved

i = \sqrt{- 1} = \pm 1

but I {don}^{'} t remember how \dots that guy was

seriously convinced \dots as I stated before :

t h o s e w h o k n o w n o t h i n g m u s t b e l i e v e e v e r y t h i n g

Commented by MJS_new last updated on 06/Aug/21

\dots on the other hand

f (x) = \frac{x}{x}

\lim_{x \to 0} f (x) = 1 \Rightarrow \frac{0}{0} = 1

g (x) = \frac{2 x}{x}

\lim_{x \to 0} g (x) = 2 \Rightarrow \frac{0}{0} = 2

\frac{0}{0} = 1 \land \frac{0}{0} = 2 \Rightarrow 1 = 2 q . e . d .

now {what}^{'} s you argument Mr . Peter Frank ?

Commented by MJS_new last updated on 06/Aug/21

��

Commented by iloveisrael last updated on 06/Aug/21

the other way

\lim_{x \to 0} \frac{\sin x}{x} = 1 = \frac{0}{0}

\lim_{x \to 0} \frac{\tan (4 x)}{2 x} = 2 = \frac{0}{0}

then 1 = 2

Commented by Olaf_Thorendsen last updated on 06/Aug/21

1 = \sqrt{1}

1 = \sqrt{(- 1) \times (- 1)}

1 = \sqrt{- 1} \times \sqrt{- 1}

1 = i \times i = i^{2} = - 1

1 = - 1

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

but its correct dans Z / 2 Z

Commented by MJS_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 {through}^{″} them while we

start to study)

Commented by ajfour last updated on 06/Aug/21

2^{n d} s t e p t o 3^{r d} s t e p i s n o t

a l l o w e d, t h e r e a r e c e r t a i n

r u l e s h e r e t h a t n e e d b e

f o l l o w e d . .

Commented by peter frank last updated on 06/Aug/21

n o a r g u m e n t s i r . u n d e r s t o o d

Answered by puissant last updated on 06/Aug/21

a = b

\Rightarrow a^{2} = ab

\Rightarrow a^{2} + b^{2} = b^{2} + ab

\Rightarrow a^{2} + b^{2} - 2 ab = b^{2} - ab

\Rightarrow {2 a}^{2} - 2 ab = b^{2} - ab car a = b

\Rightarrow 2 a (a - b) = a (a - b)

\Rightarrow 2 a = a soit 2 = 1 \dots

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