READING: I §1 7
Back to reading:
I §1 6
begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] §1. SETS AND ELEMENTS. SUBSETS. "end quote
These pages assume that the reader has the book and is reading along. topic index contents
Please read these notes from the beginning to here, and then paragraph 7 of §1.
THE EMPTY SET
The last paragraph of section one is about the empty set, which Rosenlicht defines in the next quote. I have always called it the null set, but Rosenlicht has eliminated a 'host of mathematical synonyms' (see the third paragraph of his preface), and I think this is a good elimination. I note that 'null' is the German word for zero, and Rosenlicht warns us here not to confuse the empty set with zero. He also warns us that both the empty set and zero are something - so that the empty set and zero should not be confused with nothing.
begin quote ita-1-1-6-pg3 "
The empty set is the set with no elements. It is denoted by the symbol .
I think I can improve on Rosenlicht's explanation that the empty set is a subset of every set. First, it will be very useful to have the first two paragraphs from section two.