Hey there! Let me unpack Halmos' comment for you—your confusion makes total sense, because that line about generality and depth is deeply tied to the specific context of his book, not the entire field of set theory.

First, let's clarify what Halmos was referring to when he called set theory "not very deep": his book is focused on naive set theory as a foundational tool—the core concepts (sets, functions, cardinality, ordinals) that every branch of mathematics relies on. This foundational layer is intentionally general; it's designed to be usable across algebra, analysis, topology, and more. When he says it's "less deep," he means this foundational subset of set theory prioritizes broad applicability over digging into the highly specialized, complex questions that define research-level set theory.

It's crucial to distinguish between the introductory material in Halmos' book and the wider field of set theory:

• The "general" part he's talking about is the basic framework that acts as a common language for all math. This is indeed broad, but it's only the tip of the iceberg.
• Once you move past naive set theory into axiomatic set theory (like ZFC), or topics like large cardinals, forcing, or descriptive set theory, you're entering territory that's extraordinarily deep. These areas involve highly abstract reasoning, intricate proof techniques, and open questions that have stumped mathematicians for decades—hardly "shallow."

Another angle: Halmos' comment is also setting expectations for his readers. He wrote Naive Set Theory as a primer for people who want to understand set theory's role as a foundation, not as a guide to advanced set theory research. So he's letting you know upfront that this book won't dive into the deep, niche corners of the field—instead, it's building the general toolbox you'll need for other math subjects.

Your feeling that the ideas seem deep is totally valid! For someone new to abstract math, concepts like cardinality (especially infinite cardinality) or ordinal numbers can feel wildly counterintuitive and complex. That's a different kind of "depth" than the specialized research depth Halmos is contrasting with generality. You're encountering the cognitive load of learning a new, abstract language, which is absolutely challenging—even if it's the "general" foundational layer.

备注：内容来源于stack exchange，提问作者Link L