let a = b

[callumacrae]

let a = b
-> a^2 = b^2 = ab
-> a^2 - b^2 = a^2 - ab
-> (a+b)(a-b) = a(a-b)
divide by (a-b)...
-> a+b = a
as b=a..
-> a+a = a
-> 2a = a
divide by a..
-> 2 = 1
-> 1 = 0 (-1)
-> a = 0 (*a)

This proves that 1=2, 0=1, and in general, any number is equal to 0.

...im confused

~Callum

 

[Gouri]

let a = b
-> a^2 = b^2 = ab
-> a^2 - b^2 = a^2 - ab
-> (a+b)(a-b) = a(a-b)
divide by (a-b)...
-> a+b = a
as b=a..
-> a+a = a
-> 2a = a
divide by a..
-> 2 = 1
-> 1 = 0 (-1)
-> a = 0 (*a)

This proves that 1=2, 0=1, and in general, any number is equal to 0.

...im confused

~Callum

In mathematics you can't divide anything by zero

In the above

you said

divide by (a-b)...

That can't be done as a=b you can't divide by (a-b) as it is dividing by zero.

that is mistake in the whole process.

 

[ChatIndia]

This is the puzzle in the first few pages on "mathematical games and puzzles" by Rajesh kumar Thakur. I've already seen this absurd problem.

 

[callumacrae]

In mathematics you can't divide anything by zero

In the above

you said



That can't be done as a=b you can't divide by (a-b) as it is dividing by zero.

that is mistake in the whole process.

You can, anything divided by 0 is Infinity

~Callum

 

[Gouri]

You can, anything divided by 0 is Infinity

~Callum

then in that step the equation becomes

infinity = infinity

then where the remaining steps comes from.....

 

[callumacrae]

Yey all fixed

I am no longer confused

~Callum

 

[ChatIndia]

If you wish I'll prove this using complex number concept as well. lol

 

[descalzo]

You can, anything divided by 0 is Infinity

~Callum

So,

/ 0 =

 

[ChatIndia]

-1/1 = 1/-1

taking square root on both sides

(-1/1)^1/2 = (1/-1)^1/2

now as i^2 = -1

i/1 = 1/i

now dividing by 2 on both sides

i/2 = 1/2i

adding 3/2i on both sides

and now multiplying by i on both sides

i^2/2 +3/2 = 1/2 + 3/2

-1/2 + 3/2 = 4/2

1= 2

---------- Post added at 07:07 PM ---------- Previous post was at 07:06 PM ----------

gsonline going to find fault in this.

---------- Post added at 07:16 PM ---------- Previous post was at 07:07 PM ----------

I would like to correct gsonline. "in mathematics we cannot divide by zero". Its infinity as said by alex. Actually we don't have discovered what 0/0 is yet. (a+b)(a-b)/(a-b)

= (a+b)0/0

= 0/0

did you get the mistake.

 

[callumacrae]

By (-1/1)^1/2 I'm assuming you mean (-1/1)^(1/2)?

I like complex numbers

~Callum

 

[ChatIndia]

Correct!