Full Idea
It is easy to fall into the error of supposing that a relation which is both transitive and symmetrical must also be reflexive.
Gist of Idea
A relation is not reflexive, just because it is transitive and symmetrical
Source
David Bostock (Intermediate Logic [1997], 4.7)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.176
A Reaction
Compare Idea 14430! Transivity will take you there, and symmetricality will get you back, but that doesn't entitle you to take the shortcut?
Related Idea
Idea 14430 If a relation is symmetrical and transitive, it has to be reflexive [Russell]