How to choose between a set and a tuple? Sometimes when writing pseudocodes in a paper I need to write statements of the form:


*

*$A\gets\emptyset$ (initialization);

*$A\gets A\cup\{i\}$ (add element $i$);

*$|A|$ (calculate the cardinality);


which work fine with a set $A$. 
The problem is that sometimes I need to access the $i$th element of a set $A$, $a_i$. What I understand is that there no such thing for sets. I mean I cannot write $a_i$ for the set $A$ unless the set $A$ is totally ordered. I decided to define everything from the beginning. So, I add a sentence like "All sets used in the pseudocodes are ordered. But, my supervisor told me why I do not simply use tuples? My question is that which one I should use, sets or tuples? 
With a tuple $B$, I can absolutely write $b_i$ to access the $i$th element of $B$ but I afraid that I can write the following:


*

*$B\gets\emptyset$ (initialize the tuple to be empty);

*$B\gets B\cup\{i\}$ (add element $i$ to the tuple);

*$|B|$ (get the cardinality of the tuple $B$);

 A: Many implementations of sets are ordered:


*

*Java's TreeSet and the C++ STL set template both require that the set's elements are of an orderable type (or at least that you provide a comparator), which makes the ordering directly based on that of the element.

*Since version 3.6, the Python implementation of sets preserves insertion order for the purposes of stuff like iteration and pop, though in 3.6 this is considered an implementation detail that is not to be relied upon.


I have a question for you though: why do you care about the index of items in the set?  Is there something else going on here?  Would something like pop suffice?  Would something like iteration in arbitrary order suffice?  Nowadays most languages of my acquaintance tend to prefer non-index-based iteration anyway:
in C++, for has a construction that accepts anything that has an iterator:
for (const auto& a: A) { 
   ...do something with a...
}
In Python, for is always about the iterator and if you really want indexes you'll actually use enumerate to get that:
for a in A:
    ...do something with a...

