User blog comment:Boboris02/Large number combinatorics II:Trying to prove something interesting/@comment-30118230-20170204183225/@comment-1605058-20170204192837

Since you want an opinion, I will give one. A harsh, but honest one. By trying to express it in a formal manner, you have made it almost illegible. For example, you use many symbols which aren't part of standard mathematical language, like \(\prec\) and \(\top,\bot\).

Apart from that, many descriptions you give are difficult to understand as well. What does \([S-]\#\) mean? What are these \(T\) and \(V_k\), sets, strings, functions? What does "mapped in correspondence" mean? In what way is \(S_1^*\) an ordered tuple? The Kleene's star doesn't give a set ordered in any way (also, it's usually defined for sets of strings). When you write \(\hat{\bigcup}S1\), you mention "some condition", but what condition is that? No such is mentioned e.g. when you talk about \(\hat{\bigcup}P^*\). Also, what do you understand with a string being "homeomorphically embeddable" in another string?

To not be exclusively devastating, let me mention that what you use \(\hat{\bigcup}\) actually has a standard notation, namely.