Transfinite rationals

Transfinite Equations in Transfinite Strings

F - Expansions of rationals

The ergodic theorem has been used to deduce results about the F-expansions of almost all x in (0, 1)". A simple lemma from measure theory yields some corresponding statements about the expansions of the rationals, a set of measure zero.

Transfinite Diameter

The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...

Transfinite rewriting

We survey the basic concepts and properties of transfinite rewriting for orthogonal term rewrite systems, lambda calculus, higher-order rewrite systems, and abstract rewrite systems.

Embedding trees in the rationals.

An example is presented of a simple algebraic statement whose truth cannot be decided within the framework of ordinary mathematics, i.e., the statement is independent of the usual axiomatizations of set theory. The statement asserts that every tree-like ordering of power equal to or less than the first uncountable cardinal can be embedded homomorphically into the rationals.