Thompson's group 
is the group under composition of
increasing piecewise linear homeomorphisms
of ![[0,1]](/images/equations/ThompsonsGroupF/Inline2.svg)
having finitely many pieces, dyadic rational breakpoints,
and slopes that are integral powers of 2. A dyadic rational
has the form 
for integers 
and 
. The maps fix both endpoints
of the interval.
Thompson's group 
is distinct from the sporadic Thompson group.
