Now we have Contain link, that is going from container to conteined.
That means that for example if container is set A, we have:
{
A ↦ 1,
A ↦ 2,
A ↦ 3,
A ↦ 4,
}
That leads to a contradiction, that A ↦ 1 and A ↦ 2 cannot exist at the same time, thus it is not possible to combine them into a single function.
On the other hand, if we change the direction:
{
1 ↦ A,
2 ↦ A,
3 ↦ A,
4 ↦ A,
}
We can correctly define a set using links, and we have function f(element) = A for element = 1, or 2, or 3, or 4.
The name Contain also implies that it goes from container to conteined, that means we need not only another direction, but also need different name for new link type for example IsContainedBy.
IsContainedBy will go from conteined to container and it will be aligned with current math traditions.
Now we have
Containlink, that is going fromcontainertoconteined.That means that for example if container is set A, we have:
That leads to a contradiction, that
A ↦ 1andA ↦ 2cannot exist at the same time, thus it is not possible to combine them into a single function.On the other hand, if we change the direction:
We can correctly define a set using links, and we have function
f(element) = Aforelement = 1, or 2, or 3, or 4.The name
Containalso implies that it goes fromcontainertoconteined, that means we need not only another direction, but also need different name for new link type for exampleIsContainedBy.IsContainedBywill go fromconteinedtocontainerand it will be aligned with current math traditions.