Converting a list to a set changes element order

Question

Recently I noticed that when I am converting a list to set the order of elements is changed and is sorted by character.

Consider this examp

Answer 1

In mathematics, there are sets and ordered sets (osets).

• set: an unordered container of unique elements (Implemented)
• oset: an ordered container of unique elements (NotImplemented)

In Python, only sets are directly implemented. We can emulate osets with regular dict keys (3.7+).

Given

a = [1, 2, 20, 6, 210, 2, 1]
b = {2, 6}

Code

oset = dict.fromkeys(a).keys()
# dict_keys([1, 2, 20, 6, 210])

Demo

Replicates are removed, insertion-order is preserved.

list(oset)
# [1, 2, 20, 6, 210]

Set-like operations on dict keys.

oset - b
# {1, 20, 210}

oset | b
# {1, 2, 5, 6, 20, 210}

oset & b
# {2, 6}

oset ^ b
# {1, 5, 20, 210}

---

Details

Note: an unordered structure does not preclude ordered elements. Rather, maintained order is not guaranteed. Example:

assert {1, 2, 3} == {2, 3, 1}                    # sets (order is ignored)

assert [1, 2, 3] != [2, 3, 1]                    # lists (order is guaranteed)

One may be pleased to discover that a list and multiset (mset) are two more fascinating, mathematical data structures:

• list: an ordered container of elements that permits replicates (Implemented)
• mset: an unordered container of elements that permits replicates (NotImplemented)*

Summary

Container | Ordered | Unique | Implemented
----------|---------|--------|------------
set       |    n    |    y   |     y
oset      |    y    |    y   |     n
list      |    y    |    n   |     y
mset      |    n    |    n   |     n*  

^{*A multiset can be indirectly emulated with collections.Counter(), a dict-like mapping of multiplicities (counts).}