Here’s one for you Mrs Clean – and Ugo – to practice your Algebra with.
The proof that 2 = 1
START with: a = b
multiply this by: a
gives: a2 = ab (a squared = ab))
now multiply by: – b2 (minus b squared)
this gives: a2 – b2 = ab – b2
Simplify this [difference of two squares]: (a + b)(a – b) = b (a – b)
remove the same terms from both sides of the equation [i.e. remove the expression (a – b) ]
gives: (a + b) = b
BUT if a = b which we started with – then (a + b) = b must mean that 2 = 1
Q.E.D
I thank you.