Two Rivers, Culture and Life

Here is an excerpt from Michael Steinhardt's book 'No Bull-my life in and out of markets' , which is of much inspiration in understanding the American and immigration culture.

"In looking back on my career and my life, I can see that my values, and the goals I continue to strive for, represent the confluence of two great rivers: The age-old river of Judaism, the people and the tradition, and the river of secularized (societies are no longer under the control or influence of religion) American. From the Eastern European Jewish river flows a region, and, more importantly, a culture, while from the other river flows twentieth and twenty-first century American life with its openness, social mobility, and material prosperity. I believe my generation of Jews, in particular, is the product of these same two rivers, and the contents of both are strong within us. But, over time, the American river has grown stronger, becoming dominant in our lives, while the Eastern European river has been subsumed (to include something in a particular group and not consider it separately). For the first 50-plus year of my life, I too traveled, almost exclusively, along the secular river of American culture. Now I work, almost exclusively, on strengthening the flow of the river of my heritage."

       --'No Bull-my life in and out of markets', Chaper 17, pp.263.

On Property

The word property is not easy to define precisely.
According to Merriam Webster: 'property' can be interpreted as:

(a) A quality or trait belonging and especially peculiar to an individual or thing;
(b) An effect that an object has on another object or on the senses;
(c) An attribute common to all members of a class.

More simple, according to Google Dictionary:
(a) A thing or things that are owned by somebody; a possession or possessions;
(b) A quality or characteristic that something has.

Mathematically, however, we shall not hesitate to use it in the usual (informal) fashion.
If P denotes a property that is meaningful for a collection of elements, then we agree to write {x : P(x)} for the set of all elements x for which the property P holds. We usually read this as "the set of all x such that P(x)". It is often worthwhile to specify which elements we are testing for the property P. Hence we shall often write:

{x  S : P(x)} for the subset of S for which the property P holds.