User blog comment:Boboris02/Large number combinatorics II:Trying to prove something interesting/@comment-2033667-20170206081115/@comment-2033667-20170208000242


 * I did call it a set,but that's just because I wanted to describe it as a set with that property

just write "\(S \in \mathbb{N}^*\)", which is formally sound and unambiguously communicates your meaning (provided that you specify that * represents the kleene star). a string is not a kind of set.

okay, moving forward to [S]T, which "adds 1 to all elements of the string S." your choice of notation is odd and confusing. T is a function, so just write T(S). don't deviate from standard notations unless you have a good reason. aside from that i understand what it means, so that's fine.

next we get to [S]T-, which goes completely off the rails. i don't understand what it means at all. i suggest you attempt to rephrase this definition with the following guidelines:


 * don't cram multiple definitions into a sentence. put the definitions in separate lines even, so it's really clear where one begins and the other ends.
 * avoid unconventional use of symbols. i assume you're defining a function here named "T-" -- don't do that. call it "U" or something.
 * as i said earlier, call a function a function.

can you give me examples of what T, T-, and S- do ?