High Quality Content by WIKIPEDIA articles! Wheels are a kind of algebra where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring. Also the Riemann sphere can be extended to a wheel by adjoining an element 0 / 0. The Riemann sphere is an extension of the complex plane by an element infty, where z/0=infty for any complex zneq 0. However, 0 / 0 is still undefined on the Riemann sphere, but defined in wheels. Wheels discard the usual notion of division being a binary operator, replacing it with a unary operator / x similar (but not identical) to the reciprocal x ? 1 such that a / b becomes short-hand for a cdot /b = /b cdot a, and modifies the rules of algebra such that * 0x neq 0 in the general case. * x - x neq 0 in the general case. X/x neq 1 in the general case, as / x is not the same as the multiplicative inverse of x.

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