[Math] In what context are these mathematical symbols used

notation

I just noticed that the Unicode character set contains an entire block (256 characters) of math symbols. I've got no idea how some of them should be used. For example:

  • U+22DA (⋚) and U+22DB (⋛): less-than-equal-to-or-greater-than, and greater-than-equal-to-or-less-than. Why not just use the good old equals sign = ?
  • U+2295 through U+2298 (⊕⊖⊗⊘): circled + − × ⁄ symbols
  • U+2235 (∿): sine wave; why do we need a character for this? does anyone use this?
  • U+2268 (≨): less-than-but-not-equal-to; isn't this redundant? if x < y then isn't it always true the x ≠ y?

I got these from here (you can click "more").

Thanks!

Best Answer

$\oplus$ and $\otimes$ are used to denote direct sum and tensor product, which are ubiquitous in mathematics. They also have a pedagogical use as symbols for addition in an abstract abelian group resp. multiplication in an abstract group when you want to make the point that groups are much more general than addition and multiplication of real or complex numbers. $\ominus$ is occasionally used in this abstract way as well.