Mathematical illusions

When we were driving from Poland we stopped by Anykey in Linköping, Sweden, since SmallOne couldn't come to Midgard Developer Meeting in Poland. It's always so nice to visit that placid place.

While driving to Stockholm we (me, Rambo and Bergie) were pondering on Midgard Position (it's going to replace GPS as soon as we launch our Midgard satellites) what should be the sophisticated guess to start the bracketing of the closest locations and how quickly should the square (or rectangular, since we still haven't given it a thought how to prevent North-South axis from growing a lot faster close to poles) grow.

That discussion reminded me of a mathematical illusion. Try to figure out what goes wrong, when I prove that 3 = 2.

       a + b = c               || +2a + 2b

     3a + 3b = 2a + 2b + c     || -3c

3a + 3b - 3c = 2a + 2b - 2c

3(a + b - c) = 2(a + b - c)

       <=> 3 = 2, q.e.d.