>> Fact: It is impossible to determine whether two arbitrary expressions 
>> are equivilent.
> 
>   Define expression.
> 
>   (And for that matter, define "equivilent".)

It is impossible to determine whether two arbitrary terms in the untyped 
lambda calculus are extensionally equivilent.

But is it possible to determine if some arbitrary term matches a 
predetermined one? (For example, the Church numeral zero.)

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