Does the Union Notation in Abstract Algebra Allow for Multiple Matches for x?

In summary, the conversation discusses a question about the union notation and its meaning. The asker is confused about whether the "or" in the notation allows for more than one match for x. The expert clarifies that "or" always means non-exclusive or.
  • #1
freefizix
2
0
This question links to a former discussion on the board. I'm confused regarding this thread:

https://www.physicsforums.com/showthread.php?t=3622"

Specifically, towards the end of the thread, the asker states (in regards to the union notation originally cited):

"...if we say that x is an element of the union of those sets, then we know x is an element of at least one of those sets. "

I thought the "or" conditional of the union meant that one (and only one) match occurs for x for the notation to be true. I could be wrong...:biggrin:
 
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  • #2
Nope. "Or" always means non-exclusive or.
 
  • #3
Got it, thanks...
 

1. What is Abstract Algebra?

Abstract Algebra is a branch of mathematics that studies algebraic structures. It deals with sets and operations on those sets, as well as the properties and relationships between those sets.

2. What are some examples of algebraic structures studied in Abstract Algebra?

Examples of algebraic structures include groups, rings, fields, and vector spaces. These structures have specific operations and properties that are studied in Abstract Algebra.

3. How is Abstract Algebra different from regular Algebra?

Abstract Algebra is more abstract and general than regular Algebra. It studies algebraic structures as a whole, rather than focusing on specific equations or formulas. It also uses more advanced concepts and notation, such as group theory and category theory.

4. What are some real-world applications of Abstract Algebra?

Abstract Algebra has many applications in fields such as computer science, physics, and cryptography. It can be used to analyze and solve problems related to symmetry, patterns, and data structures.

5. Do I need a strong background in math to understand Abstract Algebra?

While a strong foundation in math is helpful, it is not necessary to have a deep understanding of calculus or other advanced math topics to understand Abstract Algebra. However, a basic understanding of algebraic concepts and notation is required.

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