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roger
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whats a ring ?
What is a Cartesian Product of R with Itself?
- Thread starter roger
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In summary, the Cartesian Product of R with itself is a mathematical operation that combines each element of a set R with every other element in that same set, resulting in a new set of ordered pairs. This product is often denoted as R x R and is useful in understanding the relationships between elements in a set and can be extended to higher dimensions. It is an important concept in set theory and has applications in various fields of mathematics and computer science.
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- #3
roger
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dextercioby said:
yes, i also looked at that site too.. but I don't understand it all.
What did you mean by r^2 by the way ?
and do rings have relevance to physics ??
- #4
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I didn't see any [itex] r^{2}[/itex]...
Yes,they do.Theoretical physics uses abstract algebra a lot.
Daniel.
Yes,they do.Theoretical physics uses abstract algebra a lot.
Daniel.
- #5
Vanes63
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Abstract Algebra
Take a set, give it a few properties, that's what most of abstract algebra is about.
A ring is just one of the structures that is studied in abstract/modern algebra.
Start with groups, then it will get you to identify what a ring is a little better.
- Vanes.
Take a set, give it a few properties, that's what most of abstract algebra is about.
A ring is just one of the structures that is studied in abstract/modern algebra.
Start with groups, then it will get you to identify what a ring is a little better.
- Vanes.
- #6
roger
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dextercioby said:I didn't see any [itex] r^{2}[/itex]...
Yes,they do.Theoretical physics uses abstract algebra a lot.
Daniel.
How do you get started studying rings though ?
I wanted to know what you meant by R^2 when you showed me the double integral..in the other homework question.
- #7
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Aaaaa,got it.You've studied cartesian (direct) product.It's the cartesian product of R with itself.
You should have introductory abstract algebra in high-school.If not,then definitely in college,if u take a math major.
Daniel.
You should have introductory abstract algebra in high-school.If not,then definitely in college,if u take a math major.
Daniel.
FAQ: What is a Cartesian Product of R with Itself?
What is a Cartesian Product of R with Itself?
A Cartesian Product of R with itself is a mathematical operation that combines each element of a set with each element of the same set. In other words, it is the set of all possible ordered pairs of elements from the original set.
How is a Cartesian Product of R with Itself calculated?
The Cartesian Product of R with itself is calculated by multiplying each element of the original set by each element of the same set. For example, if the set is {1, 2, 3}, the Cartesian Product of R with itself would be {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}.
What is the significance of the Cartesian Product of R with Itself?
The Cartesian Product of R with itself is significant in mathematics because it allows for the representation of complex data sets and relationships between them. It is also used in many fields, including computer science and statistics, to analyze and interpret large amounts of data.
How is the Cartesian Product of R with Itself different from other mathematical operations?
The Cartesian Product of R with itself is different from other mathematical operations, such as addition or multiplication, because it combines elements from the same set rather than performing operations on them. It also results in a set of ordered pairs rather than a single value.
Can the Cartesian Product of R with Itself be applied to sets of any size?
Yes, the Cartesian Product of R with itself can be applied to sets of any size. However, as the size of the sets increases, the resulting Cartesian Product also increases exponentially, making it more difficult to work with and analyze.