Lexicon of Arguments

 

Thiel I 200
Def Similar/Similarity/Mathematics/Thiel: A set A ordered by the relationship K is similar to a set B ordered by K',
if A can be mapped on B in such a way that the images b1, b2, in each case two elements a1, a2, from A which stand in the relationship a1Ka2, the relationship b1K'b2 applies to the images b1, b2.
This similarity proves to be an equivalence relation, so that we look for statements about ordered sets, which are valid not only by them, but also by similar ones.
>Equivalence.
An abstraction step leads to the "type of order" (Mp) represented by the pair term "(M,p)".
>Abstraction, >Sets, >Set theory.
I 200/201
It does not follow from this that the order types must also have typical properties of the numbers, e.g. of the basic numbers. Some, of course, do.
Order types: often, however, behave little "numerically". For example, the sum and product of two order types can only be explained similarly to the basic numbers if the properties of commutativity and distributivity are dispensed with.
>Distribution.
For example, the inverse sequence (s) of the basic numbers is not similar to the sequence of the basic numbers in so far as it has one last element, the other not. Therefore we do not call order types ordinal numbers.
>Well.ordered.