In this chapter, we focus on the language
aspect of logic; the reasoning aspect is investigated in
Appendix Proving. A third aspect, the automatization of
problem solving on computers, is discussed in another
course "Logic for Computer Science".
(2)
Logical constants can be considered as connectives of arity
0, i.e., as connectives that do not take any arguments.
(3)
See the followup comments on the definition of
"union" and "powerset".
(4)
This does not contradict the statement that for every positive
n in N, there is a unique pair -n in Z and +n in Z. Rather it shows us that the union of two disjoint copies of an infinite
set S still has the same size as S, i.e., that our intuition of
set sizes cannot be automatically applied to the infinite case.
(5)
In computer
science, trees grow downwards! ;-)
(6)
The corresponding propositions may be nevertheless true.
