- #1
Cinitiator
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Homework Statement
Which branch(es) of mathematics predominate in these equations (see pic below)?
Which branch(es) of mathematics predominate in these equations?
- Thread starter Cinitiator
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In summary, the conversation discusses the use of notation in mathematical equations and attempts to identify the branches of mathematics that the equations belong to. The conversation touches on topics such as set theory, complex function theory, and graph theory. The use of the strange greater than sign and the min and max operators are also discussed. The conversation concludes with an explanation of how the min and max operators work and their relation to previously defined ordering on a set. The branches of mathematics that are mentioned include set theory and possibly complex algebra.
Which branch(es) of mathematics predominate in these equations (see pic below)?
- #2
conquest
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It might help to define big S small s and possibly the weird bigger then sign with subscript j (ordering of some kind?).
It looks now like some set theory with some (possibly partial) ordering. The use of 'arg' suggests some complex function theory or just complex algebra.
It looks now like some set theory with some (possibly partial) ordering. The use of 'arg' suggests some complex function theory or just complex algebra.
- #3
Dickfore
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maybe Graph Theory.
- #4
Cinitiator
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conquest said:
As far as I know, the big S is a set. I'm also wondering about the strange bigger than sign too. Which branch of mathematics does it come from? I can recognize lots of set theory notation here, but some notation (such as the strange greater than sign) doesn't make sense to me.
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- #5
Office_Shredder
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If you want us to help you with the notation it would be really useful if you post the full context under which this is occurring
- #6
Cinitiator
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Office_Shredder said:
I've lost the original source - all I know is that it's from an economics paper. What I'm particularly interested in are these strange greater than signs, as well as max and min operators. Which branch do they come from? Well, I'm familiar with max and min parameters, but not when they have some parameters under them.
- #7
Office_Shredder
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The greater than sign is probably some previously defined ordering on a set
min means exactly what you think it means. The fact that there is an i=1,2 underneath it means take the minimum of the expression where the value of i can be either 1 or 2.
For example
[tex] \min_{i=1,2,3} i = 1[/tex]
[tex] \min_{i=3,4,5} 1/(i-6) = -1[/tex]
min means exactly what you think it means. The fact that there is an i=1,2 underneath it means take the minimum of the expression where the value of i can be either 1 or 2.
For example
[tex] \min_{i=1,2,3} i = 1[/tex]
[tex] \min_{i=3,4,5} 1/(i-6) = -1[/tex]
- #8
Cinitiator
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Office_Shredder said:
Thanks a lot, this helped. However, what exactly do you mean by 'some previously defined ordering on a set'? I know that you can use Cartesian product to create n-tuple relations out of 2 sets and give them order, and that you can simply use n-tuples as well as sequences to express an ordered set of data. Is it related to these concepts, or is it something completely different?
Also, which branch of mathematics do the min and max operators come from?
FAQ: Which branch(es) of mathematics predominate in these equations?
1. What is the purpose of identifying the predominant branch(es) of mathematics in equations?
Identifying the predominant branch(es) of mathematics in equations allows for a deeper understanding of the underlying principles and concepts being utilized in the problem. It also helps in choosing the appropriate methods and techniques to solve the equations.
2. How do you determine which branch(es) of mathematics is dominant in an equation?
To determine the dominant branch(es) of mathematics in an equation, you must first identify the operations and symbols present. Different branches of mathematics use specific operations and symbols, so this can give clues as to which branch is being used. Additionally, you can analyze the structure and patterns of the equations, as well as the context in which they are being used, to identify the predominant branch.
3. Are there equations that use multiple branches of mathematics?
Yes, there are many equations that use multiple branches of mathematics. In fact, most real-life problems require the use of multiple branches of mathematics to solve. For example, physics problems often involve both algebra and calculus, while economics problems may involve both statistics and geometry.
4. What are some common branches of mathematics found in equations?
Some common branches of mathematics found in equations include algebra, geometry, trigonometry, calculus, statistics, and linear algebra. However, there are many other branches of mathematics that may be used in specific fields or applications.
5. Can identifying the predominant branch(es) of mathematics in equations make solving them easier?
Yes, identifying the predominant branch(es) of mathematics in equations can make solving them easier. This is because it allows you to focus on specific techniques and methods that are commonly used in that branch of mathematics. It also helps in avoiding unnecessary or incorrect methods that may not be applicable to the problem at hand.