Combination of a Smile and a Frown ....

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In summary, in the discussion on the construction of the rational numbers in Bloch: The Real Numbers and Real Analysis, a symbol for an equivalence relation is introduced in Definition 1.5.1 and Lemma 1.5.2. This symbol combines a \smile and a \frown and can be coded as \asymp in Latex. There is also the option to use Detexify LaTeX handwritten symbol recognition for future reference.
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In Bloch: The Real Numbers and Real Analysis we find, in the discussion on the construction of the rational numbers, a symbol for an equivalence relation that looks like a combination of a \smile and a \frown ... the symbol appears in Definition 1.5.1 and Lemma 1.5.2 below ... View attachment 7026Can anyone tell me the Latex code to form this symbol ...?

Peter
 
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We have it as a symbol in our Quick $\LaTeX$ element, in the Algebra section, with the toolltip "Asymptotic To"...the code is:

\asymp

which produces:

\(\displaystyle \asymp\)
 
  • #3
MarkFL said:
We have it as a symbol in our Quick $\LaTeX$ element, in the Algebra section, with the toolltip "Asymptotic To"...the code is:

\asymp

which produces:

\(\displaystyle \asymp\)
Thanks Mark ...

Must go to the Linear and Abstract Algebra forum and get the guide ... the guide I have been using is the one from MHF ...

Peter
 
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MarkFL said:
This is what I meant:
Sorry Mark ... my silly confusion ...

... or since you guys are in the USA ... should I say, my bad ...

Peter
 
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FAQ: Combination of a Smile and a Frown ....

What is the psychological significance of a combination of a smile and a frown?

The combination of a smile and a frown, also known as a "smile-frown" or "smirk," can have different meanings depending on the context and individual. It can represent conflicting emotions, such as feeling happy and sad at the same time, or it can be a way to express sarcasm or irony. It can also indicate a sense of uncertainty or ambivalence towards a situation or person.

Is there a specific muscle or facial expression associated with a smile-frown?

The smile-frown is not a distinct facial expression, but rather a combination of two separate expressions: a smile and a frown. These expressions involve different muscles, with a smile typically involving the zygomaticus major muscle and a frown involving the corrugator supercilii muscle.

Can a smile-frown be perceived differently in different cultures?

Yes, the interpretation of a smile-frown can vary across cultures. In some cultures, a smile-frown may be seen as a sign of insincerity or deception, while in others it may be seen as a way to convey subtle emotions or playfulness. It is important to consider cultural differences when interpreting facial expressions.

How does a smile-frown affect communication and social interactions?

A smile-frown can add complexity to communication and social interactions. It can convey mixed emotions and make it more difficult for others to accurately interpret one's feelings. In some cases, it may also lead to misunderstandings or conflicts if the intended meaning is not understood by others.

Are there any common misconceptions about the smile-frown?

One common misconception is that a smile-frown always indicates insincerity or deceit. While this can be the case, it is not the only possible interpretation. As with any facial expression, the meaning of a smile-frown can vary and should be interpreted in the context of the situation and individual's body language and verbal cues.

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