suppose that an infinite subset $a$ of the natural numbers is partitioned into finitely many subsets. a property of $a$ that is always inherited by at least one of the elements of the partition is known as a partition regular property. suppose we have a method of measuring the size of an infinite subset of the natural numbers. a property $p$ is said to be a density property if every infinite subset of the natural numbers which is large enough, according to our yardstick, satisfies $p$. in the qualitative sense, partition regular properties guarantee that order is conserved and density properties guarantee that order is always achieved at a threshold size. we will provide some interesting examples and applications of partition regular properties, density properties, and related ideas.