Re: Simple enough for every reader?

On 09.07.2025 10:34, Mikko wrote:

On 2025-07-08 15:47:12 +0000, WM said:
 

On 08.07.2025 09:46, Mikko wrote:

On 2025-07-07 15:37:08 +0000, WM said:
 

On 07.07.2025 10:29, Mikko wrote:
 

Bijection requires completeness of domain and codomain.

 So you say but cannot prove.

 It is so by definition. See e.g. W. Mückenheim: "Mathematik für die ersten Semester", 4th ed., De Gruyter, Berlin (2015).

 Can you refer to some better author?

 That is hardly feasible. But you can look up the definition in every textbook of your choice. You will find the same result. Even Wikipedia will be sufficient: a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set.

 So no requirement of completeness.

 "Each element" means that none is missing.

 No, it does not. What is said about each element applies to missing
elements, too.
 

In mathematics, a surjective function (also known as surjection, or onto function is a function f such that, for every element y of the function's codomain, ... [Wiki]

There is none missing.