  Fair division with unequal shares is an intensively studied recourse
allocation problem. For $ i\in [n] $, let $ \mu_i $ be an atomless probability
measure on the measurable space $(C,\mathcal{S}) $ and let $ t_i $ be positive
numbers (entitlements) with $ \sum_{i=1}^{n}t_i=1 $. A fair division is a
partition of $ C $ into sets $ S_i\in \mathcal{S} $ with $ \mu_i(S_i)\geq t_i$
for every $ i\in [n] $.
  We introduce new algorithms to solve the fair division problem with
irrational entitlements. They are based on the classical Last diminisher
technique and we believe that they are simpler than the known methods. Then we
show that a fair division always exists even for infinitely many players.
