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X^2 is a weird way to describe it. A function f is idempotent if f(f(x)) = f(x).
by pdpi 6y ago
X^2 is a weird way to describe it. A function f is idempotent if f(f(x)) = f(x).
- creata 6y agoIt's not that weird. People often write iterated composition as f^k, and this is especially true with matrices, where composition and multiplication mean the same thing.
- corty 6y agoIt is quite common in some fields. Operator application is written without parentheses, and functions are a kind of operator. Therefore: f(x) = f(f(x)) = f f x = f^2 x = f x And leaving out the x, because it is just a placeholder anyways: f f = f^2 = f And of course this means that f^n = f because f^n-1 f = f^n-1 by induction.
- lamontcg 6y agoDepends on if you think of functional notation or matrix operators and linear algebra first. There's also dirac bra-ket notation from QM. I tend to reach for the latter two more than the former. Particularly in this case O^2 = O makes more sense to me than f(f(x)) = f(x). And I just naturally think about A B - B A = 0 rather than f(g(x)) - g(f(x)) = 0 for commutativity.