The things you can do with maths

Is this proof that 2 = 1?

If x = 1 and y = 1 then x = y

STEP 1

Multiply each side by x

x² = xy

STEP 2

Subtract y2 from each side

x² - y² = xy - y²

STEP 3

Factor each side

(x + y)(x - y) = y(x - y)

STEP 4

Divide out the common term (x - y)

x + y = y

STEP 5

Substitute the values of x and y

1 + 1 = 1

so,

2 = 1