# Re: [tlaplus] Defining Cardinality with TLA

 P.S.: Proofs of these theorems checked by TLAPS are given in https://github.com/tlaplus/tlapm/blob/main/library/FiniteSetTheorems_proofs.tla.On 26 Apr 2024, at 06:37, Stephan Merz wrote:As Markus pointed out, cardinality of finite sets is defined in a standard module of TLA+. A collection of lemmas about finite sets and cardinality, useful for actually reasoning about these notions, is available at https://github.com/tlaplus/tlapm/blob/main/library/FiniteSetTheorems.tla (included in the distribution of TLAPS).StephanOn 26 Apr 2024, at 02:22, marta zhango wrote:Is the line IN  CS[S]part of the definition of cardinality ?On Friday, April 26, 2024 at 11:55:57 AM UTC+12 Markus Kuppe wrote:https://github.com/tlaplus/tlaplus/blob/03c7bf4f35ccf1217ac2c53e5bf60d1220c8b0d8/tlatools/org.lamport.tlatools/src/tla2sany/StandardModules/FiniteSets.tla#L21-L27 > On Apr 25, 2024, at 4:53 PM, marta zhango wrote: > > Have thought something like this too > > Cardinality(set) == (+ e \in DOMAIN set: IF set[e] THEN 1 ELSE 0) > > On Friday, April 26, 2024 at 9:17:00 AM UTC+12 marta zhango wrote: > Like this for instance ? > > Cardinality (S) = |S| == Count ( e \in S ) > > > On Friday, April 26, 2024 at 8:36:13 AM UTC+12 marta zhango wrote: > How can I define the cardinality of a set as the number of elements in a set S > using the notation |S| using TLA. -- You received this message because you are subscribed to the Google Groups "tlaplus" group. To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/f2c82e65-92e1-4c06-b61a-dfd78d19a017n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "tlaplus" group. To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/B9A5CC33-3D90-4BDD-9D26-7A489F3AFD88%40gmail.com.