For example, if you feed {x|xεZ,0<x} to it,
it returns { 1,2,3,4,5,6,7,8,9,10,11,…}
For example, if you feed {x|xεZ,0<x} to it, it returns { 1,2,3,4,5,6,7,8,9,10,11,…}
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
For example, if you feed {x|xεZ,0<x} to it,
it returns { 1,2,3,4,5,6,7,8,9,10,11,…}
I don’t know of any such software.
Note that no general algorithm for enumerating arbitrary sets can exist; a program that accepts any set written in set-builder notation must also be able to solve e.g. the halting problem. Moreover there exist sets that cannot be enumerated even theoretically, for example those whose construction requires use of a choice function on the reals.
Naturally the problem is easier if you restrict what kind of expressions can appear in the set-builder notation, but even then anything more complex than linear inequalities is surprisingly hard. For instance, it is known that no algorithm exists to determine whether or not a polynomial equality
P(x_1, ..., x_9)=0in nine variables has an integer solution (this is an extension of Hilbert’s 10th problem), never mind actually finding some exemplar solutions.