The Puzzle Page is dedicated to bringing you the best puzzles collected from around the world along with original puzzles not seen anywhere else.

The staff at The Puzzle Page always enjoy seeing new puzzles and would love to hear from you. If you have a puzzle that's giving you problems, drop us a line -- we'd love to help.





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?

11 comments:

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

Gaurav 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.

Heyentah 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.

Kushla 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.