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begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] 4. FINITE AND INFINITE SETS. "end quote
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Please read these notes from the beginning to here and then paragraph 1 of 4.


As I was working on 3, I looked ahead to this section and thought that it would be best to postpone it until after the second chapter on the real number system. However, it is very interesting and the only prerequisite seems to be an ability to count: 1,2,3,... any many. Therefore, please ...

begin quote ita-1-4-1-pg10 "
We are familiar with the set of positive integers, or natural numbers   {1,2,3,...}.   This set, together with the various ideas associated with it, such as its ordering (the fact that its elements can be written down [or recited] in a definite order), or such as the fact that two of its elements may be added to get a third with certain general rules holding for this addition, can be obtained from the primitive principles of set theory. In this text we shall instead assume the basic properties of the real number system and from those derive all the properties of the set   {1,2,3,...}.   In this section we shall for convenience assume a few simple facts about the natural numbers in order to get as quickly as possible to certain other easy matters of set theory. However all the facts about the set of natural numbers that are used here will be proved explicitly in the next chapter. The notions developed in this section will not be applied until later, so no circular reasoning occurs.
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