# RE Bad terms in seq A108719? (last one)

Tautócrona tautocrona at terra.es
Tue Nov 15 00:58:42 CET 2005

```----- Original Message -----
From: <franktaw at netscape.net>

Yes.  All members of the empty set are prime.  All members of the empty set are composite.
All members of the empty set are pink elephants.  This is standard mathematical usage, and
for very good reasons.

-----------------------------------

Ok, now I see the flaw in my thinking. It was like that:

1. Formal logic is consistent, that is, we can't have p and -p to be tautologies at the
same time.
2. Let p be "All members of the empty set are prime". Then -p is "At least one member of
the empty set is not a prime".
3. If q is "All members of the empty set are composites" then another way of saying q is
"No member of the empty set is a prime".
4. If no member of the empty set is a prime, then we can assure that at least one member
of the empty set is not a prime, therefore we have that q --> -p
5. If we have p & q then as q --> -p we have p & -p. So we cant have p & q.

The flaw is, of course, in 5.). If we have that q --> -p then we know that Q is a subset
of -P, not the other way around. So we can not infer from q --> -p and p & q that we have
p & -p because P & Q is a set smaller than P & -P (I hope the logic-set theory analogy is
clear for anyone). I applied a false modus.

At least it served to me to have another sophism of my own invention - I collect them and
present them as exercises to my friends and pupils :-)

Regards. Jose Brox

```