The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Math Topics »

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: How much set theory is needed for geometry?
Replies: 5   Last Post: Feb 29, 2008 11:10 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Frederick Williams

Posts: 238
Registered: 5/31/07
How much set theory is needed for geometry?
Posted: Feb 15, 2008 10:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

I make reference to Coxeter, _Introduction to Geometry_, Wiley, Second

In section 12.2 _Intermediacy_ , Coxeter discusses the relation
[ABC]--informally "point B is between points A and C"--and then he
defines segment, interval, ray and line as sets using that relation.

Not much set theory seems to be needed, but how much? If one were to
formalize this set theory should it be a theory with points as

Would one do better to formalize it using many-sorted first order logic
with points, segments, intervals, rays and lines as sorts?

In either case, what then about triangles and other plane figures?

Going forward at this moment in time a raft of measures
have been put in place on the ground to target and
claw back the growth of cliche usage 24/7.
Remove "antispam" and ".invalid" for e-mail address.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.