Re: Galileo's Paradox and the Project of the Reals

cbrown@xxxxxxxxxxxxxxxxx wrote:
Tony Orlow wrote:

Okay, define me an infinite set which doesn't use successor or order in
the definition, or in the definition of something used in the definition.


The set of all lines in the Euclidean plane.

Define "line" without '<'.


Or:

The set of all triangles in the Euclidean plane.

Define "triangle" without "line".


Neither of these sets has a "standard" ordering which allows us to say,
for any two elements a, b (lines or triangles) that exactly one of a <
b, a > b or a = b holds true.

Cheers - Chas


No, in the 2D plane, one needs to use something like a lexicographic ordering by ordering the dimensions of the space, and then using the order within each dimension.

Tall Ho!

Tony
.

Relevant Pages