let a = b

callumacrae

not alex mac
Community Support
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

Community Paragon
Community Support
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

Community Support
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

not alex mac
Community Support
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

Community Paragon
Community Support
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.....

Last edited:

callumacrae

not alex mac
Community Support
Yey all fixed

I am no longer confused

~Callum

ChatIndia

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

descalzo

Grim Squeaker
Community Support
You can, anything divided by 0 is Infinity

~Callum

So,

/ 0 =

ChatIndia

Community Support
-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

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

not alex mac
Community Support
By (-1/1)^1/2 I'm assuming you mean (-1/1)^(1/2)?

I like complex numbers

~Callum