I'm writing a paper and I've come across interesting problem. In my algorithm, I create a list of 0's (example [0,0,0,0]), where the number of 0's is given by parameter "x". Later I want to update these values using argmin to get the smallest member of this set/list and assign it new value. The problem is how to succinctly describe the creation of such set/list in pseudocode, i.e., mathematical notation.

From what I know, I can't use set, since there are duplicate elements. List have nonstandard notation of add operation and they look weird and there is no notation like "Set-builder" for sets to make the creation of starting list of zeroes in one line. Multi-sets are not very distinguishable from actual sets in notation, which makes it bit confusing for the reader, not mentioning that "Set-builder" notation does not contain what I need to describe it anyway.

I just can't figure out a good way how to deal with this problem.

  • 1
    $\begingroup$ You say "pseudocode, i.e., mathematical notation", but pseudocode has different conventions and options from the mathematical notation in the vast majority of math papers that do not use pseudocode. 1. Can you confirm that you want pseudocode rather than a non-pseudocode mathematical presentation? 2. It's unclear if the order of the numbers in your list matters to you, or what you do when multiple entries attain the lowest value. $\endgroup$
    – Mark S.
    May 8 at 11:05
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    $\begingroup$ @MarkS. I'm sorry I was unclear, I want pseudocode. The order of numbers does not matter to me, however I use argmin in my code to extract the reference to element of minimal value. When I think about it I didn't really think about cases where multiple elements have the minimal value - if argmin is still returning one element or a "subset". $\endgroup$
    – eXPRESS
    May 8 at 14:20

So my current solution to this problem is as follows:

$MultisetOfZeroes \gets \{0\} \rightarrow x$

I'm not sure if it is correct however if I understood this answer correctly it should be applicable like that.


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