quantities and predicates are just the axioms 8 and 9 of the Zermelo-Fraenkel set theory provides a close connection. We now want particular predicates, called hernehmen links, and thus amounts to miss an algebraic structure.
this, we want to clarify what is a link. This requires a small forward. We are working with quantities. We can fairly easily from our naive intuition use a lot, we must also be aware that we are in an emergency, namely, when the conventional idea of a set can lead to contradictions, to look at Zermelo-Fraenkel, whether the look set to that effect at all is a lot in this sense .
The
Cartesian product
a set A with set B is the set of ordered pairs (a, b) with
and
For example, for 
and
the Cartesian product 
The Cartesian product of A with itself 
A
relation R between two sets A and B is a subset of the Cartesian product Figure 1. A Figure f from A to B is a relation in which there is exactly one for each Photo3 Photo4. relations based on the above sets A and B are the following amounts:
figures are below the following amounts:
figures from A to B are including the following amounts:
images of A to A, the following amounts:
A binary logic f is a map from a Cartesian product two sets A and B in a further quantity of C. We write to us now especially interested in the inner binary logic
. These are binary logic in which A = B = C. We remain so all the time in the same amount. It does nothing more than to any pair of elements of A an element of A clearly assigned. Let M be a set and f an internal binary operation of M. Then we call the pair (M, f)
a
magma. The magma is a basic structure of algebra. As we shall see, some important algebraic structures special cases of the magma.
A classic example of a magma is the set of integers with the usual subtraction. If you subtract any two given integers from one another, we get a clear result, which is again an integer.
The natural numbers arise with the usual addition of a magma.
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