The Ω combinator leads to non-terminating recursion by calling itself indefinitely, highlighting the concept of infinite loops in lambda calculus without a base case.
In contrast, the Y combinator facilitates recursive expressions, allowing termination through fixed-point combinators, using a function g that recurs correctly.
Applying Y to a function g expands to g(Y(g)), which illustrates how Y(g) embodies recursion by linking each function call back to itself.
The Y combinator essentially redefines recursive function calls in lambda calculus, highlighting a fundamental property of functional programming in handling recursion.
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