Can You Prove That 1=2 ? Is it Possible ?
Yes It is possible to prove that 1 = 2 .Some Assumptions are necessary to prove that any mathematical equations and theorems. for example 0! = 1; 1^0 = 1, These are called magic numbers . using this we can also prove 1 = 2 . Two methods are given here to prove this equation. but still several methods are there to prove this . post the possible solutions through comments on this post.
Method 1
a^2 – b^2 = (a+b) (a-b) ——- Eqn 1
a^2 – a^2 = (a+a) (a-a) ——- Eqn 2
a^2 – a^2 = a (a-a) ——- Eqn 3
Equate 2 and 3
a (a-a) = (a+a) (a-a)
=> a = (a+a)
If a =1 then 1 = (1+1)
=> 1 = 2 (Proved)
Method 2
If a^m = b^n then
m =n
1^0 = 1^1
=> 0 = 1
Add one on both sides
0+1 = 1+1
=> 1 = 2 (Proved)

Cheating!
The first method is like:
1*0 = 0
2*0 = 0
So, 1*0 = 2*0
So, 1 = 2 <== Not allowed to divide by 0.
The second method:
if that is true then why not simply write:
1^1 = 1
1^2 = 1
So, 1^1 = 1^2
So, 1 = 2 <== Not allowed for base 1.