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Definition 1.1.2 Define the set S to be the smallest set contained in N and satisfying the following two properties:

  1. 0 ∈ S, and
  2. if n ∈ S, then n + 3 ∈ S

Here is to define the set of 0,3,6… And then say that smallest set is necessary, otherwise there are many such sets.
Exercise 1.3

Find a set T of natural numbers such that 0 ∈ T, and whenever n ∈ T,
then n + 3 ∈ T, but T != S, where S is the set defined in definition 1.1.2.

Give an example of T?

Answer 0:

All natural numbers set N can.

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