An atomic proposition $\perp$ sometimes included in a language as a representation of an absurd or contradictory proposition, dual to the other Church constant $\top$. In axiomatizations of intuitionistic logic, falsum is often employed in defining intuitionistic negation, so that $\neg \phi$ can be defined as $\phi \to \perp$. In some settings, both $\perp$ and the Ackermann constant f correspond to falsehood. The two are distinguished on the basis of their interpretation: $\perp$ is interpreted as standing in for the infinitary conjunction of all contradictions (or formulae in general) while $f$ is interpreted as the infinitary disjunction of all contradictions, i.e., $\perp$ is read as ‘all contradictions are true’ while $f$ is understood as ‘some contradiction is true’. In a paraconsistent setting, the truth of one contradiction does not entail the truth of all contradictions, whence $\perp$ is strictly stronger than $f$. In classical or intuitionistic logic, however, the two notions converge and $\perp$ and $f$ become equivalent.