Symbol \stackrel{\smile}{\frown}: Meaning & LaTeX Command?

In summary, the symbol \stackrel{\smile}{\frown} is a mathematical symbol that represents a smile or a frown. It is used to indicate the positive or negative direction of a graph or a function. To type this symbol in LaTeX, the command \stackrel{\smile}{\frown} is used. It can also be customized in terms of size, font, and color. In mathematics, it is used to represent positivity and negativity, concavity and convexity, and various other concepts. Other similar symbols include \overset{\smile}{\frown}, \overbrace{\frown}, and \underbrace{\smile}, which have similar meanings but may differ slightly in appearance and usage
  • #1
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I just was wondering what is the meaning of this symbol
[itex]\stackrel{\smile}{\frown}
[/itex].
It is used in the terminology of estimation of norms, I do not know if it is a standard notation, since I did not find anymore explanations. Also I do not know if there is a command to write it directly by LaTeX instead of "\stackrel{\smile}{\frown}".
Thanks in advance.
 
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  • #2
I just have found the symbol, so now the question is
what does it mean?
[itex]\asymp[/itex].
 

1. What is the meaning of the symbol \stackrel{\smile}{\frown}?

The symbol \stackrel{\smile}{\frown} is a mathematical symbol that represents a smile or a frown. It is often used to indicate the positive or negative direction of a graph or a function.

2. How do you type the symbol \stackrel{\smile}{\frown} in LaTeX?

To type the symbol \stackrel{\smile}{\frown} in LaTeX, you need to use the command \stackrel{\smile}{\frown}. This command requires the use of the amsmath package. Alternatively, you can also use the command \smile or \frown to type just the smile or frown symbol respectively.

3. Can the symbol \stackrel{\smile}{\frown} be customized in LaTeX?

Yes, the symbol \stackrel{\smile}{\frown} can be customized in LaTeX by changing its size, font, and color. This can be done by using the appropriate commands such as \scalebox, \textcolor, and \textsf, respectively.

4. How is the symbol \stackrel{\smile}{\frown} used in mathematics?

The symbol \stackrel{\smile}{\frown} is used in mathematics to represent various concepts such as positivity and negativity, concavity and convexity, and the direction of a curve. It is also used in set theory and logic to represent the subset and implication operations, respectively.

5. Are there any other similar symbols to \stackrel{\smile}{\frown}?

Yes, there are other similar symbols to \stackrel{\smile}{\frown} such as \overset{\smile}{\frown}, \overbrace{\frown}, and \underbrace{\smile}. These symbols have similar meanings and can be used in different contexts in mathematics. However, they may have slight differences in appearance and usage.

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