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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.    
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Please read these notes from the beginning to here.

READING SUBSET SYMBOLS

The double arrow provided an example where we need to read both from right to left and from left to right. The symbols that are used to express the subset relationship provide a situation where we can say the relationship in just one way if we read in both directions.

begin quote ita-1-1-6-pg3 "
[...]
  or  
[...]
  or  
"end quote

If it is understood that both X and Y are upper case, then we can read both sides of the first line as 'X is a subset of Y', and we can read both sides of the second line as 'X is not a subset of Y'.

Also: It will be very useful to talk here about the symbol that is used between numbers to indicate which one is smaller or bigger than the other.

You may see     or   . These symbols always point to the smaller number.

Now, if you make the pointed end round, you can see the subset symbol, and the rounded end always points to the 'smaller' set - where the 'smaller' set is the one all of whose elements are in the set on the other side of the symbol.

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