- #1
wisvuze
- 372
- 1
Hello, I was wondering if there were alternative definitions to a "function" ( alternative to the standard f is a subset of A X B if f : A -> B ).
I was introduced to the "general" definition of a cartesian product ( with respect to an indexing set H ) , it is weird to me because the general cartesian product is defined as a set of mappings, so it doesn't "quite" sync up with the standard "tuple" cartesian product of sets ( indexed by natural numbers ) as a generalization.. I thought I could get around this if the definition of a mapping doesn't rely on the original definition of a cartesian product, but I cannot think of another way to define a map.
However, is it unreasonable to leave a mapping as an undefined object? I am not too familiar with the depths of set theory, so I do not know if it would lead to disastrous results..
thanks :)
I was introduced to the "general" definition of a cartesian product ( with respect to an indexing set H ) , it is weird to me because the general cartesian product is defined as a set of mappings, so it doesn't "quite" sync up with the standard "tuple" cartesian product of sets ( indexed by natural numbers ) as a generalization.. I thought I could get around this if the definition of a mapping doesn't rely on the original definition of a cartesian product, but I cannot think of another way to define a map.
However, is it unreasonable to leave a mapping as an undefined object? I am not too familiar with the depths of set theory, so I do not know if it would lead to disastrous results..
thanks :)