question about notation

Oct 2019
3
0
Southwest USA
I am an old geek trying to relearn mathematics that I knew 45 years ago. I am beginning to read a basic introduction to rigorous mathematics and need to ask a question about notation. Be patient, I am unsure whether I can use Latex to express it in this interface, so I am going to phrase it out as best that I can in English. The book expresses the set union relationship as follows:

A union B equals Left Brace x is in A pipe symbol x is in B right bracket.

Now to my knowledge, the pipe symbol in mathematics is "such that". However I would read what I think it says as:

A union B equals left brace x is in A and x is in B right brace

The author of the book is a distinguished mathematician, ergo sum I assume I am misunderstanding somehow. Can the pipe symbol be read as "and"?
nmgeek
 
Last edited by a moderator:

mathman

Forum Staff
May 2007
6,913
762
I suggest you use Latex to show what you are expressing.
 
Aug 2012
2,483
776
I am an old geek trying to relearn mathematics that I knew 45 years ago. I am beginning to read a basic introduction to rigorous mathematics and need to ask a question about notation. Be patient, I am unsure whether I can use Latex to express it in this interface, so I am going to phrase it out as best that I can in English. The book expresses the set union relationship as follows:

A union B equals Left Brace x is in A pipe symbol x is in B right bracket.
That sounds like the intersection, not the union.

$A \cup B = \{x \in A | x \in B \}$

You can quote my post to see how I did that.

Oh I see what's going on. They may be using | to mean "or" rather than "such that." That's why you need to define your symbols. But with that interpretation, this is not valid set builder notation. Perhaps this book is out of date.
 
Last edited by a moderator:
  • Like
Reactions: 1 person
Oct 2019
3
0
Southwest USA
That sounds like the intersection, not the union.

$A \cup B = \{x \in A | x \in B \}$

You can quote my post to see how I did that.

Oh I see what's going on. They may be using | to mean "or" rather than "such that." That's why you need to define your symbols. But with that interpretation, this is not valid set builder notation. Perhaps this book is out of date.
OK, one question that I had was can latex be used in this interface. It would appear that that is true.

$A \cup B = \{x \in A | x \in B \}$

is exactly what I am trying to (in my mind) translate into an English sentence. I would like to read that as "A union B equals x is in A and x is in B". However, from what I know of notation, I suspect that "A union B equals x is in A, it is true that x is in B" would be more correct. Which is more correct?
 
Oct 2019
3
0
Southwest USA
A comment

I am an older geek who has been a computer tech for many years. Recently I was forcibly retired due to health and budget reasons. I am recovering my health, living on social security and trying very hard to learn. I am NOT a mathematician. I would like to become conversant with mathematics. I am also studying Latex2e, python, bash and to a lesser extent PowerShell. I reside in the Southwest USA
nmgeek