User blog comment:P進大好きbot/Evaluation of Analysis/@comment-30754445-20181120105029/@comment-35470197-20181120220754

> Is it well defined?

Undefined. Therefore I am treating it in a similar way to UNOCF.

> My point is that when doing any kind of research, there are agreed-upon basic concepts which does not need to be explained every time they are used.

Right, as long as there is no other notion which is denoted by the same symbol in the context.

We denote by \(\mathbb{N}\) both the set of natural numbers and the set of positive integers. In order to avoid the ambiguity which can be declined by an expert with careful reading of results, journals sometimes requeire us to declare which terminology we used in the context. It does not mean that we need to define the notion of natural numbers using von Neuman construction and axiom of infinity.

There are many such kind of terminologies. Knot, zero-dimensional, compact, category, variety, and so on. There is no ambiguity if a reader is an expert who read the result deeply. In order to set the result to be accessible to anyone who sufficiently knows notions before careful reading, the choice of terminology should be declared.

> The only question is where we draw the line.

Exactly, as I explained in the example for the surjectivity.

> Obviously that would be absurd. So who gets to decide what constitutes "common knowledge in the field" which can be used without a direct reference, and what doesn't? You? A person who openly stated that when it comes to googology he is an absolute beginner?

Since I am a relative beginner for you, I can create evaluations which is written by beginner by definition :)

> But I still maintain that according to the criteria you've listed yourself, it is a level 3, and that your classification here is wrong.

Ok. Thank you.