Well, λ-terms are defined by the rules of the λ-calculus[0], or variants of it, while mathematical functions have their own, distinct definition[1]. Essentially, the axioms used to define either are fundamentally different.
Not all mathematical functions can be expressed/represented by λ-terms; a famous example would be the halting problem[2]. Generally, keep in mind that the λ-calculus — as Turing machines — can only express computable functions[3].
You could also try to think about how to perform usual mathematical function operations on λ-terms: limits, differentiation, integration, etc.
Not all mathematical functions can be expressed/represented by λ-terms; a famous example would be the halting problem[2]. Generally, keep in mind that the λ-calculus — as Turing machines — can only express computable functions[3].
You could also try to think about how to perform usual mathematical function operations on λ-terms: limits, differentiation, integration, etc.
[0]: https://en.wikipedia.org/wiki/Lambda_calculus
[1]: https://en.wikipedia.org/wiki/Function_(mathematics)
[2]: https://en.wikipedia.org/wiki/Halting_problem
[3]: https://en.wikipedia.org/wiki/Computable_function