Two exercises to which I have (really) no clue.
Explain how
Common Notions 1 and
4 may be interpreted as the
transitive and
reflexive properties.
Note that the natural way to write Common Notion 1 symbolically is slightly different from the statement of transitivity above.
Show that the
symmetric property follows from
Common Notions 1 and
4.
The book goes on to say:
"Hilbert took advantage of Common Notions 1 and 4 in his rectification of Euclid's axiom system. He defined equality of length by postulating a transitive and reflexive relation on line segments, and stated transitivity in the style of Euclid, so that the symmetric property was a consequence."
Could someone outline what he'd done (or point to other source)?