Wheel theory in the context of Division by zero

⭐ Core Definition: Wheel theory

A wheel is a type of algebra (in the sense of universal 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.

The term wheel is inspired by the topological picture $\odot$ of the real projective line together with an extra point ⊥ (bottom element) such that $\bot =0/0$ .

↓ Menu

Wheel theory in the context of Perpendicular symbol

"Up tack" is the Unicode name for a symbol (⊥, \bot in LaTeX, U+22A5 in Unicode) that is also called "bottom", "falsum", "absurdum", or "absurdity", depending on context. It is used to represent:

The truth value 'false', or a logical constant denoting a proposition in logic that is always false. (The names "falsum", "absurdum" and "absurdity" come from this context.)
The bottom element in wheel theory and lattice theory, which also represents absurdum when used for logical semantics
The bottom type in type theory, which is the bottom element in the subtype relation. This may coincide with the empty type, which represents absurdum under the Curry–Howard correspondence
The "undefined value" in quantum physics interpretations that reject counterfactual definiteness, as in (r₀,⊥)

View the full Wikipedia page for Perpendicular symbol

↑ Return to Menu

Wheel theory in the context of Division by zero

Wheel theory Study page number 1 of 1

Play TriviaQuestions Online!

Skip to study material about Wheel theory in the context of "Division by zero"

⭐ Core Definition: Wheel theory

Wheel theory in the context of Perpendicular symbol