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>>8110197
>>8110187
countably infinite:
let x denote the cardinality of the set of morally distinct trolley problems, T
the proof consists of two parts, firstly to show that x <= aleph0, secondly to show that x >= aleph0.

the first theorem is trivial. let L denote the language of trolley problems. L contains a finite number of symbols. a trolley problem is well-defined if it can be encoded in the language L in a finite number of symbols. Hence x <= set of all finite sequences generated by a finite set. hence x<= Aleph-0.

the second proof is as follows:
consider the set of trolley problems of the following form, denoted as R(x,y), were x and y are non-negative integers.

let P={ R(x,y) : x,y in N}

clearly cardinality of P = cardinality of N^2 = aleph 0 as there exists a bijection of R(x,y) onto 2-tuple x,y.

clearly P is a subset of T.

therefore x>=aleph 0.

thus completes the proof that there are a countable number of morally distinct trolley problems. QED