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I'm a beginner in set theory and I have doubt regarding mathematical induction. I came across the following examples.

Example 1:

Find the set given by the following definition:

1) $ 3 \in P $

2) For $x,y \in P, x + y \in P $

3) Only those elements obtained from steps (1) and (2) are in $P$

Solution: The set $P$ consists of positive integers which are multiples of 3.

Example 2:

Give an inductive definition of the set

$ P = \{2,3,4,\ldots\} = N - \{0,1\}$

Solution:

1) $ 2 \in P$ and $3 \in P $

2) If $x,y \in P$, then $x+y \in P$.

3) Only those elements obtained from steps 1 and 2 are in $P$.

Could anyone explain the above two examples and how to write this kind of definitions? I googled it, but couldn't get what I need. Thanks in advance.

  • 0
    Which part do you not understand?2012-08-23
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    @DanielPietrobon How did they found that the set has multiples of 3 in example 1 and how to write the definitions in Example 2, Sir?2012-08-23
  • 0
    Well, what is 3+3?2012-08-23
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    @DanielPietrobon But, they didn't mention that y is also 3, Sir.2012-08-23
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    @DanielPietrobon So, initially as they have mentioned 3 belongs to P, we take both x and y as 3. Am I right, Sir?2012-08-23
  • 0
    let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/4593/discussion-between-daniel-pietrobon-and-gomathi)2012-08-23

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