Question about this set-theory identity

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In summary, this book has a typo in the first sentence which can lead to an incorrect result. I would recommend sticking with the introduction in order to get a better understanding of the subject.
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MathematicalPhysicist
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I am reading this book:
https://web.stanford.edu/class/math285/ts-gmt.pdf
on page 2 in remark 1.5(1), it's written that:
##\cap_{j=1}^\infty A_j = X\setminus (X\setminus \cup_{j=1}^\infty A_j)##
this seems totally wrong, shouldn't it be ##X\setminus \cup_{j=1}^\infty (X\setminus A_j)## ?

I wonder if this book has other such pitfalls...
 
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I agree with you.
 
  • #3
cap and cup is a typo that can easily be made, e.g. by cut and paste. I think you cannot derive the value of an entire script from a simple typo.
 
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Proofreading a text is a tedious, thankless job that is never finished. No matter how hard one tries, there are still mistakes. If you want to minimize the chance of occasional errors, look for books that have been around for decades and have had many prior editions.
 
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FactChecker said:
Proofreading a text is a tedious, thankless job that is never finished. No matter how hard one tries, there are still mistakes. If you want to minimize the chance of occasional errors, look for books that have been around for decades and have had many prior editions.
This book was recommended for a Geometric Measure Theory course I am watching in zoom.
I am not taking the course for credit or anything like that.
A few years ago I started reading Herbert Federer's book, perhaps I should return to it.
 
  • #6
If this is your first course on the subject, I would stick with this introduction and see if you like to participate in the Zoom sessions. Federer is not an introduction but a treatise.

And I would just send a brief email to the author to let him know about what is probably a typo. (Or you can collect some more and send him a list.) Just be sure to have the current version of the book, as this is from 2014 and advertised as a draft. So the typo may already have been corrected.
 
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  • #7
S.G. Janssens said:
If this is your first course on the subject, I would stick with this introduction and see if you like to participate in the Zoom sessions. Federer is not an introduction but a treatise.

And I would just send a brief email to the author to let him know about what is probably a typo. (Or you can collect some more and send him a list.) Just be sure to have the current version of the book, as this is from 2014 and advertised as a draft. So the typo may already have been corrected.
Hi, do you know perhaps where can I find a copy of the book which did get published?
I cannot find it in Amazon.
 
  • #8
fresh_42 said:
cap and cup is a typo that can easily be made, e.g. by cut and paste. I think you cannot derive the value of an entire script from a simple typo.
I didn't derive, I wondered.
different words, big difference...
 
  • #9
I think I'll retry Federer's book.
As the saying goes:"

Fortune Favours the Brave​

"
 

1. What is a set-theory identity?

A set-theory identity is an equation that shows the relationship between two sets. It states that the two sets are equal, meaning they have the same elements.

2. What are the different types of set-theory identities?

There are three types of set-theory identities: extensional, intensional, and equality. Extensional identities focus on the elements of a set, while intensional identities focus on the properties that define a set. Equality identities show that two sets are equivalent.

3. How are set-theory identities used in mathematics?

Set-theory identities are used in mathematics to prove theorems and solve problems. They help to define and describe the properties of sets, and can be used to show the relationships between different sets.

4. What is an example of a set-theory identity?

An example of a set-theory identity is A ∪ B = B ∪ A, which states that the union of sets A and B is equal to the union of sets B and A. This identity is known as the commutative property of union.

5. How are set-theory identities related to logic?

Set-theory identities are closely related to logic, as they use logical operations such as union, intersection, and complement to define the relationships between sets. They also follow the laws of logic, such as the commutative, associative, and distributive properties.

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