I recently started reading Topology and Groupoids by Ronald Brown and this notation came up. The notations is $$[x,\to[ \; =\{z \mid x \leq z\}$$ and a similar notation for other type of intervals. I have never seen this before, and I was baffled wondering if this was a funny $\LaTeX$ macro mistake where "2" was used as "\to" in some situations. I am wondering if it is sort of common? Is it common in some area of mathematics? If it is not clear, I am asking about using the "$\to$" arrow not really the brackets (although I rarely see the bracket notation).

  • 1
    $\begingroup$ @AndresCaicedo Thanks. I was thinking when I figured out the notation that it was less deceptive than the $+\infty$ and $-\infty$ notation. Although it looks funny when writing functions with these arrow intervals, I guess no notation is perfect. You should post your comments as an answer. $\endgroup$ – Paul Plummer Jun 23 '13 at 18:47

It is not uncommon.

When discussing (partially) ordered sets, people sometimes use $\leftarrow$ and $\to$ rather than $-\infty$ and $+\infty$, so the interval $(\leftarrow,b)$ means the same as what other times one writes as $(−∞,b)$, that is, $\{z\mid z<b\}$. The use of $],[$ is also common enough (and dates back to Bourbaki), with $]a,b[$ meaning the same as $(a,b)$, etc.

Here are some examples: 1, 2.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.