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SetAndItsRelatedSequences
ABSTRACT . Draft V0: In this article, I introduce the fundamental sequence of all natural numbers and generalise
the notion of sequence and subsequence. Then I introduce set from its related sequences which are:
(1) its generating sequences
(2) its canonical sequences
(3) its image sequences
After highlighting the main differences between a set and its related sequences, I reveal common confusions
between a set and its canonical sequences in set theory. This article includes:
(1) Fundamental sequence and generalisation
(2) Set and its related sequence: Canonical, image sequences and generating sequences.
(3) Applying setcentrics operators to canonical sequences
(4) Reminder about a well ordered set and ordinals
(5) Showing the inconsistency between 2 Venn diagram representations of the same sets (ordered and disor
dered)
(6) Proposal: the wellordered generating or image sequence of the nonorderable set
(7) Conclusion