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In this chapter, we take a closer look at Peano Arithmetic (PA) which we have defined in Chapter 1. In particular, we prove within PA some basic arithmetical results, starting with the commutativity and associativity of addition and multiplication, culminating in some results about coprimality. This paves the way for the coding of finite sequences of numbers, which will be covered in the next chapter.

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Arithmetic in Peano Arithmetic

  • 章节

  • 发表日期：

    2025年

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  • Lorenz Halbeisen,
  • Regula Krapf

摘要

In this chapter, we take a closer look at Peano Arithmetic (PA) which we have defined in Chapter 1. In particular, we prove within PA some basic arithmetical results, starting with the commutativity and associativity of addition and multiplication, culminating in some results about coprimality. This paves the way for the coding of finite sequences of numbers, which will be covered in the next chapter.