Parity is Discrete Transformation?

[LagrangeEuler]

Why parity is discrete transformation?
$Px=-x$
$P\psi(x)=\psi(-x)$
when $x$ is continual variable. Could you explain me difference between discrete and continual transformation?

 

[tiny-tim]

Hi LagrangeEuler!

Could you explain me difference between discrete and continual transformation?

"T is a discrete transformation" means that there's no continuous way of changing from the identity transformation to T

ie there's no system of transformations T(k) with k in [0,1], with T = T(1), I = T(0)

eg if T is space inversion, there's no half-way stage between say a left foot and a right foot