We learn numbers and counting as a process of succession. ‘Eleven’ has little real meaning to us except as ‘the number after ten’. In this chapter, we use this process of succession to define the natural numbers - to do God’s work, in Kronecker’s phrase - starting from nothing (more precisely, the empty set) and progressing from one number to the next. As succession is the defining characteristic of natural numbers, so induction is the key proof technique. We can use it to define the arithmetic operations and to prove their basic properties.
KeywordsNatural Number Ordinal Number Infinite Sequence Cardinal Number Lexicographic Product
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