Both more commonly used and less standardized than ⊗, this symbol has several uses, all somehow related to saying "like + only different":

In middle schools in some parts of the world, used to signify modulo addition: After setting the modulus (say 12), you can say "7⊕6=1" instead of the more formidable "7+6=1 (mod 12)".

Computer science makes up new names for everything, but here they steal an idea from middle schools. "⊕" is often used as a symbol for the XOR operation. XOR is just modulo 2 addition. You'll also see "⊕" as a "vectorized" XOR, usually bitwise XOR on some register.

- In abstract algebra, signifies the
*direct sum* of two objects (typically modules). It's really just a finite version of cartesian product (denoted by ×, just to confuse). So A_{1}⊕...⊕A_{n} is to all intents and purposes A_{1}×...×A_{n}. The *infinite* version, however, considers only elements that are in all but finitely many positions. So
A_{1}⊕A_{2}⊕... =
{(a_{1},a_{2},...)∈A_{1}×A_{2}×.. | ∃N.∀n>N.a_{n}=0}

Your browser and/or font may not be up to the task of displaying it! It looks like a "+" (plus) in a circle...