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 A1⊕...⊕An is to all intents and purposes A1×...×An. The infinite version, however, considers only elements that are 0 in all but finitely many positions. So
A1⊕A2⊕... =
{(a1,a2,...)∈A1×A2×.. | ∃N.∀n>N.an=0}
Your browser and/or font may not be up to the task of displaying it! It looks like a "+" (plus) in a circle...