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Polymer
Polymer
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I just started reading "The calculi of lambda conversion" by Church.

Church defines functions like: id x = x, and says the domain and range are understood to be as permissible as possible. Permitting even itself, id id = id

In my experience, I've always been told to specify a domain and range with the functions I've defined. And they are usually relatively limited, in contrast to id.

This is the first time I've seen functions with a domain and range this large. Are there uses for functions with wide domains and ranges in mathematical contexts other then logic or lambda calculus.?

I just started reading "The calculi of lambda conversion" by Church.

Church defines functions like: id x = x, and says the domain and range are understood to be as permissible as possible. Permitting even itself, id id = id

In my experience, I've always been told to specify a domain and range with the functions I've defined. And they are usually relatively limited, in contrast to id.

This is the first time I've seen functions with a domain and range this large. Are there uses for functions with wide domains and ranges in mathematical contexts other then logic or lambda calculus.

I just started reading "The calculi of lambda conversion" by Church.

Church defines functions like: id x = x, and says the domain and range are understood to be as permissible as possible. Permitting even itself, id id = id

In my experience, I've always been told to specify a domain and range with the functions I've defined. And they are usually relatively limited, in contrast to id.

This is the first time I've seen functions with a domain and range this large. Are there uses for functions with wide domains and ranges in mathematical contexts other then logic or lambda calculus?

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Polymer
Polymer
  • 191
  • 6

I just started reading "The calculi of lambda conversion" by Church.

Church defines functions like: (B f gid x) = (f (g x) ), and says the domain and range are understood to be as permissible as possible. Permitting even itself, id id = id

I think this largely explains the qualitative difference, I feel, between functions in programming languagesIn my experience, I've always been told to specify a domain and range with the functions in Math classesI've defined.

Are there any subjects in "traditional" Math that uses this property in an interesting way? Or rather And they are usually relatively limited, why is this way of defining functions so rare? Or is it?in contrast to id.

Most of my educational backgroundThis is in subjects like Analysis, Algebra, and Differential equations, andthe first time I've never seen functions used inwith a domain and range this way beforelarge. IsAre there a nice way to connect them? If it helps, assume I know Category theoryuses for functions with wide domains and ranges in mathematical contexts other then logic or lambda calculus.

I just started reading "The calculi of lambda conversion".

Church defines functions like: (B f g x) = (f (g x) ), and says the domain and range are understood to be as permissible as possible.

I think this largely explains the qualitative difference, I feel, between functions in programming languages, and functions in Math classes.

Are there any subjects in "traditional" Math that uses this property in an interesting way? Or rather, why is this way of defining functions so rare? Or is it?

Most of my educational background is in subjects like Analysis, Algebra, and Differential equations, and I've never seen functions used in this way before. Is there a nice way to connect them? If it helps, assume I know Category theory.

I just started reading "The calculi of lambda conversion" by Church.

Church defines functions like: id x = x, and says the domain and range are understood to be as permissible as possible. Permitting even itself, id id = id

In my experience, I've always been told to specify a domain and range with the functions I've defined. And they are usually relatively limited, in contrast to id.

This is the first time I've seen functions with a domain and range this large. Are there uses for functions with wide domains and ranges in mathematical contexts other then logic or lambda calculus.

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Polymer
Polymer
  • 191
  • 6

Relationship of lambda calculus to the rest of math

I just started reading "The calculi of lambda conversion".

Church defines functions like: (B f g x) = (f (g x) ), and says the domain and range are understood to be as permissible as possible.

I think this largely explains the qualitative difference, I feel, between functions in programming languages, and functions in Math classes.

Are there any subjects in "traditional" Math that uses this property in an interesting way? Or rather, why is this way of defining functions so rare? Or is it?

Most of my educational background is in subjects like Analysis, Algebra, and Differential equations, and I've never seen functions used in this way before. Is there a nice way to connect them? If it helps, assume I know Category theory.