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Ha! This paper contains the definition of Y-Combinator:

> Y combinator: Y = λt. (λx. t (x x)) (λx. t (x x))

#TIL!

Which enables recursion

And applying the lambda to itself results in loops, afair.

Edit: It was the Omega operator that did that.

omega = Y id

where id = λx. x

(though Y Y does not normalize either, infinite looping like omega)