analytic delta | epsilon

issue since 2011
major question
unable articulate

is the relationship
recurrent (nonclosed)

given an epsilon
calculate deltas
until epsilon met
only way i arrive
at appropriate delta

is there a closed 
relationship such
able to arrive 
immediate given
a delta or epsilon

theoretically
there does not
exist one-to-one
relationship

many to many
unique delta
produce unique epsilon

yet due convergence
exist denumerable
infinite set of 
delta | epsilon pairs
gauranteed satisfy

if able choose
a rational epsilon
able form closed
immediate delta

an ongoing quest