Editing Empty product (section)

== In logic ==
[[Classical logic]] defines the operation of [[Logical conjunction|conjunction]], which is generalized to [[universal quantification]] in [[predicate calculus]], and is widely known as logical multiplication because we intuitively identify true with 1 and false with 0 and our conjunction behaves as ordinary multiplier. Multipliers can have arbitrary number of inputs. In case of 0 inputs, we have '''empty conjunction''', which is identically equal to true.

This is related to another concept in logic, [[vacuous truth]], which tells us that empty set of objects can have any property. It can be explained the way that the conjunction (as part of logic in general) deals with values less or equal 1. This means that the longer the conjunction, the higher the probability of ending up with 0. Conjunction merely checks the propositions and returns 0 (or false) as soon as one of propositions evaluates to false. Reducing the number of conjoined propositions increases the chance to pass the check and stay with 1. Particularly, if there are 0 tests or members to check, none can fail, so by default we must always succeed regardless of which propositions or member properties were to be tested.