Intereting Posts

Proof Verification: Composition of Continous Functions is Continuous
partial sum of Basel problem related to series involving Beta function
An inequality, which is supposed to be simple
Does the notion of “rotation” depend on a choice of metric?
Notions of stability for differential equations
Is infinity an odd or even number?
Isomorphism between direct sum of $\mathbb{Z}$ and $\mathbb{Z}$
$n = 2^k + 1$ is a prime iff $3^{\frac{n-1}{2}} \equiv -1 \pmod n$
If a theory has a countable $\omega$-saturated model does it need to have only countable many countable models?
On the possible values of $\sum\varepsilon_na_n$, where $\varepsilon_n=\pm1$ (i.e., changing signs of the original series)
Showing that two maps of the sphere are homotopic if their values are never antipodal
Compute this integral
how to find arc center when given two points and a radius
Number of circuits that surround the square.
Fourier Series Representation $e^{ax}$

I am looking for books with set theory and logic that is sufficient to understand mathematical analysis. I guess another question might be if there even exists such a book.

There are basically two problems I have seen in real analysis that requires set theory. They often create very big sets, but in set theory you can’t just create sets, you have to know why it is a set, in order to not get a paradox?

The second thing from set theory that is often used is the axiom of choice and zorn’s lemma.

Are there more things from set theory that is used in real analysis?(and also functional analysis)(apart from the operations of unions, intersections etc..)

- Book recommendation on plane Euclidean geometry
- Good math books to discover stuff by yourself
- Book of integrals
- Topology Exercises Books
- GRE textbooks question - calculus and linear algebra
- How to learn commutative algebra?

Are there any books that gives a good(and hopefully easy) introduction to all that is needed of set-theory in mathematical analysis?

- Does every positive rational number appear once and exactly once in the sequence $\{f^n(0)\}$ , where $f(x):=\frac1{2 \lfloor x \rfloor -x+1} $
- Proof there is a 1-1 correspondence between an uncountable set and itself minus a countable part of it
- Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
- Proof of a Proposition on Partitions and Equivalence Classes
- Book Suggestions for an Introduction to Measure Theory
- Showing any countable, dense, linear ordering is isomorphic to a subset of $\mathbb{Q}$
- Recursive Mapping
- Books on theorems of Basic set theory after Logic…?
- Standard model of ZFC and existence of model of ZFC
- Is the sets of all maps from $\mathbb{N}$ to $\mathbb{N}$ countable?

Try the first chapter of *Topology* by Munkres.

Two very standard texts on set theory are

Introduction to Set Theory by Hrbacek & Jech.

This book approaches the subject informally(not much formal logic) and has a good range of topics.

Also there is

Elements of Set Theory by Enderton.

This book requires some familiarity with formal logic and so it a bit more rigorous than Hrbacek & Jech. It doesn’t cover quite as many topics as the first book, but does cover anything you would need for real analysis.

- Evaluating the series $\sum_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} $
- How to find the value of $\sin{\dfrac{\pi}{14}}+6\sin^2{\dfrac{\pi}{14}}-8\sin^4{\dfrac{\pi}{14}}$
- Finding the Derivative of |x| using the Limit Definition
- Is $z^{-1}(e^z-1)$ surjective?
- Online classes/books in multivariable calculus?
- A metric space such that all closed balls are compact is complete.
- A possible dilogarithm identity?
- How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
- If $x$ is real and $p=\frac{3(x^2+1)}{2x-1}$, prove that $p^2-3(p+3)\ge0$
- How do I evaluate the following definite integral?
- Binomial Expression
- About the intersection of any family of connected sets
- Is there a name for the group of complex matrices with unimodular determinant?
- Z coordinates of 3rd point (vertex) of a right triangle given all data in 3D
- Finding a dual basis for the vector space of polynomials degree less than or equal to 2