Calculating Complexity with Big-O Notation

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SUMMARY

This discussion focuses on calculating complexity using Big-O notation, specifically addressing the formula \(\frac{}{<(N-n)!>} = (1 + \mathcal{O}( \frac{1}{} ))\). Participants noted issues with rendering certain mathematical expressions in browser popups, particularly the factorial notation and its HTML representation. The conversation highlights the importance of accurately displaying mathematical notations in web formats to avoid confusion.

PREREQUISITES
  • Understanding of Big-O notation and its applications in algorithm analysis
  • Familiarity with factorial notation and its mathematical implications
  • Basic knowledge of HTML rendering issues related to mathematical expressions
  • Experience with LaTeX for typesetting mathematical formulas
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  • Research the principles of Big-O notation in algorithm complexity analysis
  • Explore solutions for rendering LaTeX in web applications using MathJax
  • Learn about common HTML rendering issues and how to troubleshoot them
  • Study advanced mathematical notation and its representation in digital formats
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Mathematicians, computer scientists, web developers, and educators involved in teaching algorithm complexity and mathematical notation rendering.

Hurkyl
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[tex]\frac{<N!>}{<(N-n)!>} = <N^n> (1 + \mathcal{O}( \frac{1}{<N!>} ))[/tex]

The popup you get from clicking on this is missing lots of the code. I presume because my browser is trying to render things as HTML tags.
 
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it is missing every instance of

[tex] <N!>[/tex]

Weird.

And it is on the popup for that image. Seems to be just that one part gets dropped.
 
[tex] \begin{align*}<br /> <N!>& <N! > < N!> < N! > < N ! > <N> <N > < N> < N > <!> - \\<br /> <P!>& <P! > < P!> < P! > < P ! > <P> <P > < P> < P > <!> - \\<br /> <Q!>& <Q! > < Q!> < Q! > < Q ! > <Q> <Q > < Q> < Q > <!> - \\<br /> <I!>& <I! > < I!> < I! > < I ! > <I> <I > < I> < I > <!> - \\<br /> <U!>& <U! > < U!> < U! > < U ! > <U> <U > < U> < U > <!> - \\<br /> <B!>& <B! > < B!> < B! > < B ! > <B> <B > < B> < B > <!> <br /> \end{align*}[/tex]

[tex]<\psi>[/tex]

[tex]<\psi | H |\psi>[/tex]

Code: 
\begin{align*}
<N!>& <N! > < N!> < N! > < N ! > <N> <N > < N> < N > <!> - \\
<P!>& <P! > < P!> < P! > < P ! > <P> <P > < P> < P > <!> - \\
<Q!>& <Q! > < Q!> < Q! > < Q ! > <Q> <Q > < Q> < Q > <!> - \\
<I!>& <I! > < I!> < I! > < I ! > <I> <I > < I> < I > <!> - \\
<U!>& <U! > < U!> < U! > < U ! > <U> <U > < U> < U > <!> - \\
<B!>& <B! > < B!> < B! > < B ! > <B> <B > < B> < B > <!> 
\end{align*}
 

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