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:::: Lambda calculus is a model for computation, and numbers (and anything else computable (see [[Church–Turing thesis]])) may be represented by [[Church encoding]]. Your statements imply that Y combinator can compute the solution to fixed point equation in all cases. But all it does is simple recursion. For the case given for the definition of factorial, it terminates, but for most cases it does not. This is what I am not understanding.
[[User:Thepigdog|Thepigdog]] ([[User talk:Thepigdog|talk]]) 03:49, 10 January 2014 (UTC)
::::: The problem is only how you are trying to interpret "=". For example, the following statement (identity) is true in the lambda calculus: {{math|(λ''f''.''f'')''X'' {{=}} ''X''}}. And this is true regardless of what ''X'' is; it may be {{math|Ω}}, which is an expression that does not have a normal form, and so does not "correspond" to a computation that terminates. There is a relationship between computations and lambda expressions, but they are not the same thing. [[User:Haklo|Haklo]] ([[User talk:Haklo|talk]]) 05:41, 10 January 2014 (UTC)
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