Mar 5, 2011 · It's one common notation for stating that the left-hand side is defined as (in contrast to equal to) the expression on the right-hand side.

Dec 13, 2016 · An unsophisticated question from a neophyte: Given the numbers: $1,2,3,4,5$ What is the symbol for the range of the numbers? i.e. the lowest-highest number in the set. …

However, the middle signs in set builder (or quantifier) notation are not really catch-all replacements for the words "such that".

A better, but less common, notation is $\varepsilon$ (formatted with $\varepsilon$). You can find answers and comments related to that latter symbol $\varepsilon$ in the linked posts.

Apr 20, 2016 · So, is there any scenario where you would need to use the "↦" notation instead of "=" notation? If your answer is a full explanation, it seems to me that ↦ is entirely useless.

Dec 9, 2019 · The notation $\ {x \in \mathbb {R} \}$ is a little ambiguous, but would probably be understood. As Eike Schulte points out, there is something missing—either the "selection …

Aug 19, 2015 · The set of natural numbers $\ {0,1,2,\dots\}$ is often denoted by $\omega$. There are two caveats about this notation: It is not commonly used outside of set theory, and it might …

The (bad) notation $ (a,b)$ is often used for the greatest common divisor; somebody uses $ [a,b]$ for the lowest common multiple. Why are they bad, in particular the former? Because $ (a,b)$ …

In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical …

To summarize what has been said in the comments, there are no "official" symbols. Use whichever notation you feel most comfortable with, as long as it makes sense and can be …