Questions tagged [sets]

For questions pertaining to sets in the set-theoretical sense. Use "assignment" for questions about the use of the Mathematica functions Set or SetDelayed.

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39 views

Want to be able to determine true/false of a quantifier for proofs [closed]

Hi Mathematica community, I am trying to employ the help of mathematica to double check my work for my intro to proofs class. I want to answer and resolve a question regarding quantifiers, ...
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41 views

How to determine the domain (intersection and disjoint set) of two functions define on a set? [closed]

Suppose I have two multivariate functions $f(x,y,z)$ and $g(x,y,z)$ such that $0<x<1,0<y<1,0<z<1$. $f(x,y,z)$ is defined on values satisfying $\{0<x<1,0<y<1/2, z>y\}$ ...
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48 views

How do we express set theoretic extensionality in Mathematica for instance I want it to see {2,1} as equal to {1,2)

I think the title pretty much covers it
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2answers
165 views

Decompose set into elements?

Given a list of tuples where one element is a set: ...
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2answers
128 views

How to decompose a list of n-tuples into a union of Cartesian products

I have a list with all elements at the same level { {a, d}, {a, e}, {a, f}, {b, d}, {b, e}, {b, f}, {c, d}, {c, e}, {c, f}, {x, t}, {x, q} } How ...
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31 views

Symbolic Set Difference

Suppose I have two symbolic set containing 2-points like A={(m,n)| for m,n belonging to whole numbers}. So m,n=0,1,2,... and I have another set containing 2-points ...
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1answer
33 views

Generalizing previous question: Partition $[a,b]$ into $m$ sub-intervals and count number of sub-interval intersecting $A_1\subseteq[a,b]$?

In my previous question, How to partition $[a,b]$ into $m$ equal sub-intervals and count the number of sub-intervals that intersect with a subset of $[a,b]$?, I was given an answer to my specific ...
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1answer
78 views

How to partition $[a,b]$ into $m$ equal sub-intervals and count the number of sub-intervals that intersect with a subset of $[a,b]$?

Suppose we have a subset of $[a,b]$, where $a=0$ and $b=1$, such as $$A_1=\left\{\frac{1}{2^x}+\frac{1}{2^y}+\frac{1}{2^z}:x,y,z\in\mathbb{Z}\right\}\cap[0,1]$$ Which is a subset of $[0,1]$ If we ...
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3answers
121 views

How can I solve a Set Cover problem in Mathematica

I have $n$ non-empty possibly non-disjoint sets $S_i$, each having a cost $c_i$, and the union $\Omega=\bigcup_{i=1}^{n}S_i$. How can I find a selection of $S_i$ such that the union is also $\Omega$ ...
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4answers
147 views

How can one expand an arbitrary boolean combination into the $2^n$ atoms of the associated boolean algebra of size $2^{2^n}$?

The answer of user250938 to Can one usefully apply the Boolean functions of Mathematica to measurable Boolean sets? and the second comment of Monroe Eskew to the answer to https://mathoverflow.net/...
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1answer
81 views

Can one usefully apply the Boolean functions of Mathematica to measurable Boolean sets?

This is something of an attempted succinct/pointed rephrasing of an earlier question Given measures on sets and on certain Boolean combinations of the sets, can one check their consistency and/or ...
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34 views

Given measures on sets and on certain Boolean combinations of the sets, can one check their consistency and/or extend them to other combinations?

I have four sets--let us denote them $A_i, i=1,\ldots,4$--of quantum-information-theoretic interest (https://arxiv.org/abs/2004.06745, https://arxiv.org/abs/1905.09228). The set $A_1$ contains the ...
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3answers
85 views

every set intersection for every set in a family with another family of sets

I want to find for each list within a list of lists what intersections occur when taking set intersection for each list in another list of lists. Hopefully that makes sense. I have tried ...
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4 views

Assigning a solution to variables [duplicate]

I have solved my solution and it has been appeared, it is C1, C2, C3, C4 but when I call C1 again (%13), program shows me that C1,... is not assigned. How can I reapair that ?
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481 views

Delete sublist when sub-sublists contain same element

Given lis={{{a},{b,c,d}},{{a,b},{b,c}},{{b,c},{a,b,c}},{{b},{d}},{{a,b},{c,d}}} I want to delete sublists which have one or more elements in common. So that I ...
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2answers
796 views

How to stretch this Venn diagram?

I am trying to duplicate (approximately) the following Venn diagram in Mathematica: I have used the top of this page as a guide, which showcases the following Venn diagram triplet: ...
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1answer
101 views

ArgMin over intervals and discrete sets

I was playing with ArgMin but I'm not sure how to use it for constrained optimization. For example, ArgMin[x^2, x] returns <...
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1answer
91 views

Possible way to plot the solution density of diophantine equations

Well, I'm trying to investigate the density of solutions to Diophantine equations. What is a general method to describe that density? I've two functions: $$\varphi\left(\text{a},\text{b},\text{c}\...
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1answer
108 views

Why doesn't DeleteDuplicates do what I want

First off. I am not a mathematician I am a linguist, a syntactician who is trying to say something about semantics, which in the case at hand can be largely understood to reduce to set theory. That ...
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0answers
74 views

Is there a way to predict permutations that consist of sets?

SequencePredict is a function that predicts the next value from the arranged data. But I want to use the data for the combination to predict the next combination(...
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2answers
65 views

Making a function that takes as an input a list not care about the order of the elements of the list

I would like a function f, that takes as input a list, not care about the order of elements of the list. So,for example: f[{3,2}]=f[{2,3}] Is this possible? Or is it necessary to convert the list ...
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2answers
202 views

How to find the positions of replaced elements in a list

I have two sets of elements a={3, 4.8, 5, 4.2, 3.6, 2.3, 4.5, 3.7} b={2.8, 4.7, 5.3, 3.5, 4.7, 2.8, 4.2, 3.4} and I create ...
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1answer
69 views

Creating pairs of non-intersecting set from a given set

Let's say I have a set {a,b,c,d} and I want to create a list of pairs {{a,b,c,d},{}},{{a,b,c},{d}},{{a,b,c},{}},... such that there is no intersection between each pair, and they do not need to use ...
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1answer
128 views

Non-flat partitions of a set

A non-flat partition of a set is one where, when the elements of the set are on a grid, the partition does not contain subsets with elements from the same row. When the set is more irregular the same ...
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1answer
41 views

How to find disjoint subsets such that union of the sets give the motherset or main set?

Let us define a set $\mathcal{S}=\{1,2, 3,\cdots,67\}$. I have a list of 132 subsets. I want to obtain 16(or 17) mutually exclusive subsets such that union of such 16(or 17) is equal to $\mathcal{S}$...
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5answers
488 views

Efficient deletion of specific list entries

It is sometimes useful to remove exactly the amount of specific entries on one list from another. Consider: ...
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1answer
66 views

Calculate plausibility in Dempster-Shafer theory

I want to use Mathematica to show which subsets of a power set are required to calculate the plausibility for a given set in a power set. This has lead me to compute a summation with a ...
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2answers
212 views

Summation over an index and a set

I have an index CC and a set of values CM, and c is an element of CM and ...
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1answer
79 views

Why is Resolve not reducing my set?

I tried to run the following code to get the region where (v,b,r) satisfies some complicated set of inequalities. ...
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0answers
49 views

How to preserve braces in result

I have a result from equation, for example p={{0<=x<=1/5||x==9/10},{0<=x<=1/5||x==9/10}} and using Cases[p, z_?NumericQ -> z, Infinity] I get {0,1/5,9/10,0,1/5,9/10} But I ...
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299 views

How to add brackets to list [closed]

I have for example set of points p={1/5,1/2} and I would like to add brackets to the list, so I would like to get a set of points p2={{1/5},{1/2}} I know how to remove brackets, but I cant ...
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70 views

How to perform delayed evaluation containing function with Mathematica

I was wondering whether there is a way in Mathematica to evaluate an expression in the most simple form, without any simplifying. For example if we define: ...
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110 views

Mathematica complement of a region

I want to use Reduce Function to give me intersection of a region and complement of another region The first region is: ...
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1answer
72 views

Testing a description of the Cantor ternary set

The Cantor ternary set (aka the Cantor discontinuum) is, as usual, the set $K = \bigcap_{n=0}^{\infty} K_{n}$ where $K_{0} = [0, 1]$, the closed unit interval, and where for each $n \geq 1$ the set $...
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76 views

Iterating over pairs in a list

Take a look at this code: ...
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1answer
77 views

Operations between sets of integers [closed]

sorry it was impossible to put the code in Latex, he said that there were problems of indentation, I put the image
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0answers
47 views

Defining an abstract multiplication over finite indices

I would like to define a map (a "multiplication" denoted $\otimes$) over the finite set of symbols $G=\{a,b,c,d,e,f,g,h\}$. I would like to define several rules like $$a \otimes b= \{b \} $$ $$a \...
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1answer
67 views

Delete duplicates and sort a list of sets separately? [closed]

I have a set where it has three subsets. I want to have each element of each subsets appears only once, sorted, but the order of subsets does not change. For example: I want to get from $$ \{\{5,2,2,3\...
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3answers
873 views

Is there a simple way to perform the opposite of intersection on two lists?

By "opposite of intersection" I mean that if I have two lists like so: list1 = {1,2,4,7,9}; list2 = {1,4,9,10,11} And then we do the "Reverse Intersection" on ...
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1answer
64 views

How do I simplify operations on sets?

How would I use Mathematica to simplify: S'∩(S∪T')' The answer is S'∩T Edit: S' means Complement of S. Thanks! Solved with: BooleanConvert[! S && ! (S || ! T)]
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1answer
42 views

Set of order preserving functions

I have a partial order defined on a finite set, 13 elements, represented as a directed graph. I'm trying to work with the set of order preserving functions from this poset into a finite subset of the ...
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2answers
132 views

Finding maximal elements of partially ordered sets

I am dealing with partially ordered sets $\Gamma$, which I represent as directed graphs with an edge going from $a$ to $b$ if $a \leq b$ in $\Gamma$. For example the following graph, ...
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2answers
141 views
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0answers
138 views

Partition a set of n objects into k subsets? [duplicate]

Is there some function recently added to Mathematica that facilitates forming all partitions of a n-element set into k subsets? In other words, something that easily gives the same thing as what <...
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4answers
191 views

How to pick elements from a list with variable condition

Let A and M sets of numbers, with Length[A]=15. I want to do something like ...
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1answer
61 views

If I have numbered elements, I there a simple way to put them in a list? [duplicate]

I've defined manually 32 elements as w1, w2, w3,..., w32....
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1answer
58 views

Eliminate from list of sets those that are equal (except for the order)

I have a list of sets and some of them are equal in the sense of mathematics, but are ordered differently. How can I remove those elements from my list? For example, the set ...
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3answers
96 views

Computing $\bigcup_{n=1,5}X_{n}$? when $X_{n}=n+1,n+2,…,2n$

How do I correctly compute $\bigcup_{n=1,5}X_{n}$? when $X_{n}=n+1,n+2,...,2n$ for each $n \in \mathbb{N^{+}}$? When I do the calculation manually, I get the following results: $n=1:\{2\}$ $n=2:\{3,...
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0answers
707 views

How can I speed up my code which finds the ratio of two sums that are hard to compute? [closed]

Consider a set $\left\{\left. T(c, d)\right|c, d\in\mathbb{Z}\right\}$, a subset of the rational numbers. I want to compute $D$ $$D=\lim_{(a,b)\to(-\infty, \infty)}\lim_{(r, t)\to(\infty,\infty)}D'(...
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2answers
110 views

How to restrict a list of elements based on the values of their denominators?

EDIT: Why is my post downvoted? Can somone explain? Say we have a list of simplified elements where $$\left\{\left.\frac{(2i+1)^2}{(2z+1)^2}\right|i,z\in\mathbb{Z}\right\}\cap[1,2]$$ and we ...