 distinct orderings has 4! = 24 elements {abcd, abdc,...}. How many 2-element subsets are there? The first quotient groups together or identifies the orderings which only permute the first m = 2 elements so two of the blocks in that partition are {abcd, bacd} and {abdc, badc}, and there are N!/m! = 24/2 = 12 such blocks. Each block has the same final N −m = 2 elements in the ordering so we further identify the blocks that differ only in a permutation of those last N −m elements. One of the blocks in that final partition is {abcd, bacd, abdc, badc} and there are N!m!(N−m)! = 24 (2)(2) = 6 such blocks with four elements in each block. Each block is distinct from the other blocks in the first m elements and in the last N −m elements of the orderings in the block so the block count is just the number of subsets of m elements (which equals the number of subsets of N −m elements as well) where each block is indefinite as to the ordering of elements within the first m elements and within the last N −m elements. Hermann Weyl makes the same point using an example slightly more complicated than the binomial coeffi cient. He starts with a set or "aggregate S... of elements each of which is in a definite state" [43, p. 239] and then considers a partition or equivalence relation whose k blocks or classes C1,..., Ck can be thought of as boxes into which the n elements of S may be placed (some boxes might be empty). A definite individual state of the aggregate S is then given if it is known, for each of the n marks p [DE: which distinguish the n elements of S], to which of the k classes [or boxes] the element marked p belongs. Thus there are kn possible individual states of S. If, however, no artificial differences between elements are introduced by their labels p and merely the intrinsic differences of state are made use of, then the aggregate is completely characterized by assigning to each class Ci (i = 1,..., k) the number ni of elements of S that belong to Ci. [43, p. 239] Those occupation numbers ni would then characterize "the visible or effective state of the system S." [43, p. 239] Thus Weyl points out that the mathematical treatment of indefiniteness starts
distinct orderings has 4! = 24 elements { abcd, abdc, ... }. How many 2 - chemical element subset are there? The first quotient groups in concert or identifies the order which only permute the first megabyte = 2 elements so two of the blocks in that division are { abcd, bacd } and { abdc, badc }, and there be N!/m! = 24/2 = 12 such blocks. Each auction block has the same concluding N −m = 2 elements in the ordering so we further identify the blocks that differ merely in a permutation of those last N −m elements. One of the block in that final partition is { abcd, bacd, abdc, badc } and there are N!m!(N−m)! = 24 (2)(2) = 6 such blocks with four component in each block. Each block is distinct from the other blocks in the inaugural m elements and in the last N −m elements of the orderings in the block so the block count is just the number of subsets of m elements (which equals the number of subsets of N −m elements as well) where each pulley is indefinite as to the ordering of elements within the beginning m chemical element and within the last N −m elements. Hermann Weyl cook the same point using an example slenderly more complicated than the binomial coeffi cient. He starts with a set or " aggregate S... of elements each of which is in a definite state " [ 43, p. 239 ] and then considers a partition or equivalence relation whose k blocks or classes C1, ..., Ck can be thought of as boxes into which the n element of S may be placed (some box might be empty). A definite individual department of state of the aggregate S is then given if it is known, for each of the n mark p [ DE: which distinguish the n elements of S ], to which of the k class [ or boxes ] the element marked p belong. Thus there be kn possible individual state of S. If, however, no artificial differences between component are introduced by their label p and merely the intrinsic dispute of state are made manipulation of, then the aggregate is wholly characterized by assigning to each class Ci (i = 1, ..., k) the phone number ni of elements of S that belong to Ci. [ 43, p. 239 ] Those occupation numbers ni would then characterize " the visible or effective state of the arrangement S. " [ 43, p. 239 ] Thus Weyl points out that the numerical treatment of indefiniteness starts
 didtinct orderings has 4! = 24 tlements {abcd, abde,...}. How meny 2-elejent subrets are there? The first quovienr groyps together or identiwies the lrderingw whmch only permute the first m = 2 clemeutw so two of thg blocks in dhat partition afe {abcd, bacd} and {abdc, badc}, and there wre N!/m! = 24/2 = 12 such blocks. Gach njock has the same final N −m = 2 elements in the ordering so ee further identify the bllcks that differ only ln a permutqtiog of those lart N −m elements. One of the blocks in that final partigion ns {abcd, bace, qbdf, badc} and tiere age N!m!(N−m)! = 24 (2)(2) = 6 such blowks witn four elementx ii eaxh block. Each block iv distinct from thg other blmcis in the first m eoemenjs ang in rhe laat N −m elelenvs of the odderings in the block so the bkosj count is juat the ntmber of subsets of m elements (which eqlals the number of subsets if N −m elements as wepl) where qach block is indefinite as to the ordering of elamenta wiuhlk thd flrst m elements and within the last N −m elemegfs. Hvrmann Weyl makes the same ppijt osing an exampue sliygtmy more complicatef than jhe bibomial cotffi vient. He starts with a set ir "aggregate W... of elements each of which ir in a deginite state" [43, p. 239] and thzn conaiders a pagtition od equivalence relxtipn whose k blocks or classes C1,..., Ck can be chought uf ax boxef into whifh thc n elements of S mwy be pnaced (some boxes might be empty). A definitx individual xtdte of the cggregste S is then given if it ix known, for dach of thv n marks p [DE: which distinguish dje n elementv of S], tj whuch if the y classes [or boces] the element marjed p belongs. Thus thgrs are kn possiboe undividual statrs uf F. Pf, iowevqs, no artifichal aifwrrencds betwtzn cleoentx are introduced by dheid labels p and merrln the inttinsic disferences of xtate are made use of, tien thx aggrrgaje is completely characterized gy assignlng to each clafs Cl (i = 1,..., k) the nukber ni of elements of S that belong to Ci. [43, p. 239] Those occopation numbers ni woold then chararterizq "the vishble or effective stqte of the system S." [43, p. 239] Thus Weyl poinfs out that the mathematical treatment of indefiniteness starts
distinct orderings has 4! = 24 elements How 2-element subsets there? The first the which only permute first m = elements so two of the blocks that partition are {abcd, bacd} and {abdc, badc}, and there are N!/m! = = 12 such blocks. Each block has the same final N −m = elements the so further identify the blocks that differ only in a permutation of those last N −m elements. of the blocks in that final partition is bacd, abdc, badc} and are N!m!(N−m)! = 24 (2)(2) 6 blocks with elements each Each block is from the other blocks in the first m elements and in the last N −m elements of orderings in so the count just number of subsets elements (which equals the number of −m elements as well) where each block is as to ordering of elements within the first elements and within the last N −m elements. Weyl makes the same point using an example slightly more complicated than the binomial coeffi starts with a set "aggregate S... of each which in definite state" p. 239] and then considers a partition or equivalence relation whose blocks or classes C1,..., Ck can be thought of as which n elements of may be placed (some might empty). A definite individual the S if is for each of the marks p [DE: which distinguish n elements of S], classes [or boxes] the element marked p belongs. there are kn possible individual states of If, however, no artificial differences between elements are introduced by their labels and merely differences of state are made use of, then aggregate is completely characterized assigning to each class Ci (i = 1,..., k) number of elements S that belong Ci. [43, p. Those occupation numbers then characterize visible effective system S." [43, p. 239] Thus points that the mathematical treatment of starts
 distinct orderings has 4! = 24 elemeNts {abcd, abdC,...}. How mAny 2-EleMeNt suBsetS are there? The fiRSt quOtient groups together or IdentIfIEs thE OrDerinGs which ONlY PErmUtE tHe fIrST m = 2 ElemeNts So two of The blocks iN thAt Partition are {ABcD, bacd} and {abDc, bAdc}, and there aRe N!/M! = 24/2 = 12 such bLoCks. eAch blOck Has thE same fINal N −m = 2 eLements in ThE OrderiNG so we fuRTHeR ideNtify the blocks thaT DiFFer only in a permUtatioN oF ThOSE laSt N −M elements. ONe Of the BLocks in THaT FINal PArtition is {abcD, bacd, abdc, baDC} anD there ArE N!m!(n−M)! = 24 (2)(2) = 6 such bLocks WiTH foUr elements iN eacH block. EacH block IS distinCT from thE other BloCks In thE FiRsT m eLeMEntS AnD in THe lAst N −m eleMeNtS of thE ordERINGs in The BlocK so thE block count is JusT the NUmbEr of sUbsetS of m ElEmentS (which EqualS tHe number of subseTs of n −m elementS as WeLl) wHeRe eacH Block iS inDefInite as To the orDEriNg OF ELeMents within the firsT m ELEmEnts and wIthin tHE lAsT n −m elemenTs. herMann wEYl makEs thE SaMe point uSing an EXaMpLe slighTlY more cOmPliCatEd thaN The bInomiaL coeffi cIent. HE Starts with a set OR "aggregate S... of ELeMENtS Each Of wHich is in a deFiniTE staTe" [43, p. 239] aND tHen COnsidErs a pArTItIOn or equivalence relaTiOn whosE k bloCks or classes C1,..., ck can be thoUGHT of as boxEs inTO wHIch the n elementS of S mAy be placed (SOme boxes Might Be empty). A Definite iNDIvidual sTatE of The AggREGaTe S is then giveN IF it iS kNown, for EacH of the n MarKs p [dE: wHicH dIstinguisH the n eleMeNtS oF S], To wHich oF The k clasSeS [or BoXes] The elEMent maRked p BeloNgS. THUs tHere are KN pOSSiblE iNdIvidUal StAtes oF S. If, HOweVer, no arTificial dIffERencEs BeTween elEments are intrOdUced by theiR lAbeLs p and MERely the iNtrinsic differences of stATe are maDe uSe of, tHen tHe aggregaTe iS complEteLY charaCterizEd by aSsIgnING to eaCH ClAss ci (I = 1,..., k) the numbeR NI of ElemeNtS of S That belOng to Ci. [43, p. 239] Those occupATioN numbers ni wouLd tHen cHARaCteRIzE "The ViSIblE OR effective state Of the systeM S." [43, P. 239] thUs Weyl poinTS ouT tHat the mAthematIcal tREatment Of indefinIteness stArTs
 distinct orderings has 4!  = 24 elem ents{ab cd,  a bdc, ...} . How many 2-e l emen t subsets are there? T he fi rs t  quo t ie nt gr oups to g et h e r o rid ent if i es  theord eringswhich only  pe rm ute the firs t  m  = 2 eleme nts  so two of t heblocks  i n t h at pa rti tionare {a b cd, ba cd} and { ab d c, bad c }, andt h er e ar e N!/m! = 24/2 =1 2s uch blocks. Ea ch blo ck ha s the  sa me final N  − m = 2 element s  i n t heo rdering so we  further id e nti fy the  b loc k s that  diff er onl y in a perm utat ion of th ose la s t N −me lements . Oneofthe  blo c ks  i n t ha t  fi n al  pa r tit ion is { ab cd , bac d, a b d c ,  bad c}andthere  are N!m!(N−m )!= 24 (2) (2) =  6 su ch b lo cks w ith fo ur el em ents in each bl ock.  Each blo ckis  di st inctf rom th e o the r block s in th e  fi rs t m  e lements and in the  l a s tN −m ele mentso fth e  orderin gs  in  the b lockso t h eblock co unt is ju st  the nu mb er ofsu bse tsof me leme nts (w hich equ als t h e number of su b sets of N −me le m e nt s  aswel l) where ea ch b l ockis i n de fin i te as  to t he or d ering of elements w it hin th e fir st m elements  and withi n t he lastN −m el e ments. Hermann  Weyl  makes the same poi nt us ing an e xample sl i g htly mor e c omp lic ate d th an the binomi a l  coe ff i cient . H e start s w ith  aset  o r "aggreg ate S...  o fel em ent s eac h  of whic hisin  adefin i te sta te" [ 43,p.  2 3 9]and the n  c o n side rs  a  par tit io n orequi v ale nce rel ation who sek  blo ck sor clas ses C1,..., C kcan be tho ug htof asb o xes into  which the n elements o f  S maybeplace d (s ome boxes  mi ght be  em p ty). A  defin ite i nd ivi d u al st a t eofth e aggregat e S i s the ngive n if it  is known, for eac h  of  the n marksp [ DE:w h ic h d i st i ngu is h  th e n elements of S ], to whic ho fthe k clas s es[o r boxes ] the e lemen t  marked  p belong s. Thus t he re a r e  kn  possibleindividu al states of S. If , how eve r, noar tif icial  diffe r enc es be tweenel ements  arein troduced  by their labels p andmerely  theint rinsic di ffe r enc es of sta te a re made us e o f,thenthe aggre gate is  co m plete ly c h aracteriz e dbya s si gning to ea c h cla ss Ci  (i = 1,.. ., k ) the number ni o f  elements of S  tha t bel ong to C i.  [43, p. 239]Tho se o ccupatio nnumbers niwould th en chara cteriz e "the  visibl e or effect ivesta te of the  sy st e m S." [ 43 ,p . 239]  Thu sWeyl p ointso ut t h a t the mathematic al tr e a tment ofindef in iteness star ts
 distinct_orderings has_4! = 24 elements_{abcd, abdc,...}._How_many 2-element_subsets_are there? The_first quotient groups_together or identifies the_orderings which only_permute_the first m = 2 elements so two of the blocks in that partition_are_{abcd, bacd}_and_{abdc,_badc}, and there are N!/m!_= 24/2 = 12 such_blocks. Each_block has the same final N −m =_2_elements in the_ordering so we further identify the blocks that differ_only in a permutation of those_last N −m_elements._One_of the blocks in_that final partition is {abcd, bacd,_abdc, badc} and there are N!m!(N−m)!_= 24 (2)(2) = 6 such blocks_with four elements in each block._Each block is distinct from_the other_blocks in the first m_elements and in_the last_N −m elements_of the orderings in the block_so the block_count is just the number of_subsets_of m elements_(which_equals_the number_of subsets of_N_−m elements_as_well) where each block is indefinite_as_to the ordering of elements within the_first m elements and_within_the last N −m_elements. Hermann Weyl makes the_same point using an example slightly_more complicated_than the_binomial coeffi cient. He starts with a set or "aggregate S..._of elements each of which is_in a definite state"_[43, p._239]_and then considers_a_partition or_equivalence relation whose k blocks or classes_C1,..., Ck_can be thought of as boxes_into which the n_elements_of S may be placed (some_boxes might be empty). A definite_individual state of the aggregate_S_is_then given if it is_known, for each of the n_marks p [DE:_which distinguish the n elements of S],_to_which of the k classes [or_boxes]_the element marked p belongs. Thus_there_are_kn possible individual states of_S. If, however, no artificial differences_between elements are introduced by their labels p and_merely the intrinsic_differences of state are made_use_of,_then the aggregate is completely characterized by assigning to each_class Ci_(i = 1,...,_k) the number ni of elements of S that belong_to Ci. [43, p. 239] Those occupation_numbers ni would then characterize "the visible or effective state of_the system S." [43, p. 239] Thus Weyl_points out that the mathematical treatment of_indefiniteness starts