Difference between set and object in set theory Lately, I have started studying set theory from the "Elements of Set Theory" book. I'm just confused with the below sentence about what's the difference between set and object in set theory.

A set is a collection of things (called its members or elements), the collection being regarded as a single object.

Can I say "a set is an object"?
 A: In this quote, the only mathematical terminology is the word "set". All that's happening in that quote is that the "set" terminology is introduced, and you are provided with a hint at how to think about a mathematical "set" using your own native, human intuition. So yes, you can say that "a set is an object", but this is not a formal mathematical statement, it's just a way of talking or communicating; there is no formal mathematical content to the word "object".
This is not dissimilar with the first two lines of Euclid's Elements (following the Richard Fitzpatrick translation):

A point is that of which there is no part. 
And a line is a length without breadth.

Here, again, all that's happening is that the "point" and "line" terminologies are introduced, with hints at how to think about them intuitively, but there is no formal mathematical content to the words "part" or "length" or "breadth".
A: The PREFACE of the book
$\quad$Elements Of Set Theory
$\quad$Author:Herbert B. Enderton
begins with the opening paragraph (emphasis ours),

This is an introductory undergraduate textbook in set theory. In
mathematics these days, essentially everything is a set. Some
knowledge of set theory is a necessary part of the background everyone
needs for further study of mathematics. It is also possible to study
set theory for its own interest--it is a subject with intriguing
results about simple objects. This book starts with material that
nobody can do without. There is no end to what can be learned of set
theory, but here is a beginning.

In
CHAPTER 1
INTRODUCTION
the reader is immediately presented with the statement

A set is a collection of things (called its members or elements), the collection being regarded as a single object.

The takeaway? In the study of modern (serious/formal) mathematics, all objects, structures and 'things' can be specified using the language of set theory.
