A quick question on notation interpretation

In summary, the notation (a_n) is a bounded sequence and y_n = sup(a_k : k\geq n) represents taking the supremum of all terms of the sequence (a_n) from the n-th term forward. The k is a dummy variable used to indicate which terms are included in the set.
  • #1
122
0
Hello,

How is the following notation read?


[tex] (a_n)[/tex] is a bounded sequence. Let[tex] y_n = sup(a_k : k\geq n) [/tex]


What is meant by [tex] k\geq n [/tex]?

Thank you for your help.

M
 
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  • #2
Seems like you're dealing with limsups. Basically

[tex]y_n = \sup \{a_n, a_{n+1}, a_{n+2}, ...\},[/tex]

so that

[tex]y_1 = \sup \{a_1, a_2, a_3,... \}[/tex]
[tex]y_2 = \sup \{a_2, a_3, a_4,... \}[/tex]

etc.

In your notation, the k is just a dummy variable that tells us that all terms of the sequence (a_n) from the n-th term forward is included in the set in which we take the supremum of to get y_n.
 
  • #3
ah... thanks!
 

1. What is notation interpretation?

Notation interpretation is the process of interpreting and understanding mathematical or scientific symbols and notations used in equations, formulas, and other representations of data or information.

2. Why is notation interpretation important?

Notation interpretation is important because it allows scientists to accurately communicate complex ideas and concepts using a standardized system of symbols. It also helps to avoid misinterpretation and errors in calculations or experiments.

3. How do scientists learn notation interpretation?

Scientists learn notation interpretation through education and practice. They are taught the meanings of common symbols and how to apply them in different contexts. They also gain experience through solving problems and conducting experiments.

4. Can notation interpretation change over time?

Yes, notation interpretation can change over time as new discoveries are made and new symbols or notations are introduced. It is important for scientists to stay updated on any changes in notation interpretation within their field of study.

5. Are there different types of notation interpretation?

Yes, there are different types of notation interpretation depending on the field of study. For example, mathematical notation interpretation may be different from chemical notation interpretation. However, there are also some symbols and notations that are commonly used across multiple disciplines.

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