A note on the Harris-Kesten Theorem

Recently, a short proof of the Harris-Kesten result that the critical
probability for bond percolation in the planar square lattice is 1/2 was given,
using a sharp threshold result of Friedgut and Kalai. Here we point out that a
key part of this proof may be replaced by an argument of Russo from 1982, using
his approximate zero-one law in place of the Friedgut-Kalai result. Russo's
paper gave a new proof of the Harris-Kesten Theorem that seems to have received
little attention.