User blog comment:P進大好きbot/Kyodaisuutan System/@comment-35870936-20181003040133/@comment-35470197-20181004024754

> Syntax sugar

I meant the extension of the formal language by a definition.

Since there is no symbol like \(\lim\) in \(\epsilon \delta\) logic, we usually define a new canonical formal language and a canonical conservative extension of calculus. It is the same as the situation that we define a new canonical formal language of set theory when we deal with \(\emptyset\). (The usual formal language of set theory does not possess the symbol like \(\emptyset\).)

(In order to define what a "definition" precisely means in formal logic, we need such arguments. For example, more detailed explanations are written in the standard textbook by Kunen.)