Richard Hammack > Quotes

“Mathematics is filled with such instances where it is important to regard one set as a subset of another.”
― Richard Hammack, Book of Proof

“If a finite set has n elements, then it has 2^n
subsets.”
― Richard Hammack, Book of Proof

“In fact, any black-and-white image on the plane can be thought of as a
subset of R^2, where the black points belong to the subset and the white points do not. So the text “INFINITE” in Figure 1.4(c) is a subset of R^2 and therefore an element of P(R^2). By that token, P(R^2) contains a copy
of the page you are reading now.
Thus in addition to containing every imaginable function and every imaginable black-and-white image, P(R^2) also contains the full text of
every book that was ever written, those that are yet to be written and
those that will never be written. Inside of P(R^2) is a detailed biography of
your life, from beginning to end, as well as the biographies of all of your
unborn descendants. It is startling that the five symbols used to write P(R^2) can express such an incomprehensibly large set.
Homework: Think about P(P(R^2)).”
― Richard Hammack, Book of Proof