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I am having trouble while writing two things.

  1. I am confused how to write upper and lower limits to this.
  2. List item and how to write this in latex

anyone can help me with this?

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    Welcome to TeX.SX! Please help us help you and add a minimal working example (MWE) that illustrates your problem. Reproducing the problem and finding out what the issue is will be much easier when we see compilable code, starting with \documentclass{...} and ending with \end{document}. In other words what have you tried so far? – albert Feb 19 at 18:56
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    I'm also going to chime in with: what are you using to learn LaTeX? Subscripts with _ and superscripts with ^ are one of the first things that a LaTeX guide should let you know about. – Teepeemm Feb 19 at 19:45
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The following example shows how to write both expressions.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\( \lVert \mathbf{W} \rVert_F^2 \)

\( \min\limits_\theta \)
\end{document}

To answer more precisely your questions, the \rVert command writes the "||" character at the right of the "W", and the _ after the \rVert is used to write the following entry (F in this case) in subscript whereas the ^ after it is used to write the following entry (2 in this case) in superscript.

Also, I think I should mention that the \limits command after the \min command is not mandatory in general. It is used here because the equation is written in an inline-math environment (delimited with \(...\)). In such an environment, the equation is in \textstyle format, so by default the \theta called with \min_\theta would be typeset on the lower right corner of the "min" text, like this:

The \limits command asks to typeset the upper and lower limits on the top and on the bottom of the symbol, respectively. This behavior is often (for most symbols with limits, I think) the default in \displaystyle, which is the default format in a block-math environment (like those delimited with \[...\]). In a block-math environment, typing simply \min_\theta would give the same output as on the first image, even without the \limits command.

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