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## Thursday, January 10, 2008

### 2 = 1

Professor Egghead entered his classroom one morning when one of his undergraduate students boasted that he could prove that 2 is equal to 1. The student then showed the professor the following proof:

Given: x = 1 and y = 1 therefor:
x = y

1. Multiply each side by x:
x² = xy

2. Subtract from each side:
x²-y² = xy-y²

3. Factor each side:
(x+y)(x-y) = y(x-y)

4. Divide by the common term (x-y):
x+y = y

5. Put the initial values back in the equation:
1+1 = 1

or

2 = 1

Professor Egghead saw the problem right away, can you? Anonymous said...

Something wrong at step 3 but I can't explain it Anonymous said...

I think...

It has to do with the square of 1 still being equal to one...multiplying by 1 does not increase the value of the numbers. Anonymous said...

The problem is you cannot divide by zero and x-y is 0! Anonymous said...

you can't divide by zero Anonymous said...

the problem is between step 3 and 4
The suy has taken s-y in both sides of eqn and we know that x=y so x-y is 0.there fore we cant cancel out the term x-y becoz 0 cant be cancelled in two side...
the reason for that is say:
0 x 3=0 x 5
it doesn not mean 5 = 3..
so i found out the mistake
i should be rewarded... Anonymous said...

that is completly wrong!
x^2-y^2 is not equal to (x+y)(x-y) but to x^2+b^2-2xy!
dork Anonymous said...

that last 'anonymous'....W*H*A*T*???? Anonymous said...

the problem is step 3: the right side of the equation is incorrect. xy-y2 does not equal y(x-y). So (x-y) is not the common denominator. Anonymous said...

X=1 therefore, Y must equal something else. The point of using different letters for variables is that they represent different numbers. If that weren't true, then x=y and you stop there.

Unknown said...

If we ignore the fact that x and y technically should represent different variables and carry on...

Step one is moot. If x = 1 then multiplying both x and y by x at step one still results in 1 on both sides of the equation. Anonymous said...

please excuse my dear aunt sally, see is very old and did not mean to confuse everyone.