## Swindle? *****

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YES, you can swindle and prove theorems similar to this:

Swindle can be correctly used in many proofs, e.g.

**Irreducibility of the sphere**

**Cantor–Bernstein–Schröder theorem** ( Wiki EN )

...

Can you add the next one to the list?

A famous swindle (atributed to Samuel Eilenberg and Barry Mazur, Wiki EN) uses a foolish

1 = 1 + (−1 + 1) + (−1 + 1) + ... = 1 − 1 + 1 − 1 + ... = (1 − 1) + (1 − 1) + ... = 0

identity idea to prove various correct results in a true correct way. Read great EXPO and a DISCUSSION on Terrence Tao blog ( EN ).

= + ( + ) + ( + ) + ... =

= + + + + ... = + + + + ... =

= + ( + ) + ( + ) + ... =