>>678 補足

>> 1∈2∈3∈・・∈n∈ω
　　↓
>> 1∈2∈3∈・・∈∀n∈ω

などと、∀を使えば、よかんべ
日常数学では
「∀n∈Ｎ」は、普通だっぺ

（参考）
https://en.wikipedia.org/wiki/First-order_logic
First-order logic

First-order logic?also known as predicate logic, quantificational logic, and first-order predicate calculus?is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable.[1] This distinguishes it from propositional logic, which does not use quantifiers or relations;[2] in this sense, propositional logic is the foundation of first-order logic.

First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics.
Peano arithmetic and Zermelo?Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic. No first-order theory, however, has the strength to uniquely describe a structure with an infinite domain, such as the natural numbers or the real line.
Axiom systems that do fully describe these two structures (that is, categorical axiom systems) can be obtained in stronger logics such as second-order logic.
(引用終り)
以上