Hi. I’m having trouble following this, and since you mentioned you weren’t used to this (?) notation, I have some suggestions. They are strongly about writing style, not intended as condescension!
When you’re defining a function ‘f’, the first piece of information given is usually ‘what inputs does it take, and what outputs does it give’. This can look like:
Let A be the set of [description], and B the set of [description],
and let f : A → B, where [define what f does].
This means f takes elements of A, and returns elements that are in B, so f(s) = t means that s is in A and t is in B. We definitely can’t write f(A) = B.
Once f is defined, the letter is stuck to that definition and can’t change. if you need a vector of outputs, or a set of outputs in B, you’ll need to define a new, related function.
The looser communication style (which for some works quite well) doesn’t seem to be serving you here. A more formal style might bulletproof you against the lower sort of nitpicker such as I!
I dunno that arrows and set stuff makes even less sense to me, and if I can’t understand I can’t write it down. And as far as I’m concerned I did give what inputs each function takes and what outputs they produce.
Hi. I’m having trouble following this, and since you mentioned you weren’t used to this (?) notation, I have some suggestions. They are strongly about writing style, not intended as condescension!
When you’re defining a function ‘f’, the first piece of information given is usually ‘what inputs does it take, and what outputs does it give’. This can look like:
Let A be the set of [description], and B the set of [description],
and let f : A → B, where [define what f does].
This means f takes elements of A, and returns elements that are in B, so f(s) = t means that s is in A and t is in B. We definitely can’t write f(A) = B.
Once f is defined, the letter is stuck to that definition and can’t change. if you need a vector of outputs, or a set of outputs in B, you’ll need to define a new, related function.
The looser communication style (which for some works quite well) doesn’t seem to be serving you here. A more formal style might bulletproof you against the lower sort of nitpicker such as I!
I dunno that arrows and set stuff makes even less sense to me, and if I can’t understand I can’t write it down. And as far as I’m concerned I did give what inputs each function takes and what outputs they produce.