Our objects of study are finite state
transducers and their power for transforming infinite words. Infinite
sequences of symbols are of paramount importance in a wide range of
fields, from formal languages to pure mathematics and physics. While
finite automata for recognising and transforming languages are
well-understood, very little is known about the power of automata to
transform infinite words.

We use methods
from linear algebra and analysis to show that there is an infinite
number of atoms in the transducer degrees, that is, minimal non-trivial
degrees.