separability in different senses. That color entanglement might be linked to dark energy, too (e.g. Banerjee et al. 2005). 165Why anything rather than nothing? of the universe. In other words, the expansion of the universe is right in its appearance as the appearance of the being. However, the result of that process (the natural numbers) is given (or "granted") in advance. The creation (and quite particularly: the corresponding "principle of least action" in mechanics) suggests teleology as a certain aim, which is predefined in virtue of its necessity and embodied in the necessary appearance of the natural numbers from the empty set as an equivalent of the "nothing" to mathematics. In other words, the visibility of teleology can be understood as a "by-product" of the secondarity of the choice. The operation, which is the generation of a set from the "nothing", implies all natural numbers by the construction described in the "axiom of infinity" in set theory. The set of all natural numbers is infinite, though all natural numbers are finite according to the axiom of induction in Peano arithmetic. That last circumstance needs elucidation. First, we must understand how the axiom of induction implies that all natural numbers are finite. The unit is finite. By adding a unit to any finite number, another finite number is obtained. If both premises are true, the axiom of induction implies that all natural numbers will be finite. Furthermore, the set of all natural numbers is infinite though all natural numbers are finite. One could argue that the wholeness of all natural numbers, which is what is meant by the concept of a set, implies a new different, "emergent" property, namely to be infinite. This is in contrast to the natural numbers, constituting that wholeness, which are finite. However, as above, that wholeness, perhaps as any wholeness, is obtained by taking away from rather than by adding to the natural numbers: finiteness turns out to be more than infinity, just as finiteness turned out to be less than the "nothing", as described in the empty set earlier. One can say the following about the secondarity of choice: any set may be enumerated (the well-ordering principle), which means that it may be mapped one-to-one into some subset of the set of all natural numbers. The empty set can be enumerated by the special natural number "zero". The well-ordering principle implies the axi
separability in different senses. That color entanglement might be connect to blue energy, too (e.g. Banerjee et al. 2005). 165Why anything quite than nothing? of the universe. In other password, the expansion of the population is right in its appearance as the appearance of the being. However, the result of that process (the natural number) is given (or " granted ") in improvement. The initiation (and quite particularly: the corresponding " principle of least action " in mechanics) propose teleology as a certain aim, which is predefined in virtue of its necessity and embody in the necessary appearance of the natural numbers from the empty set as an equivalent of the " nothing " to mathematics. In early words, the visibility of teleology can be understand as a " by - product " of the secondarity of the choice. The operation, which is the coevals of a set from the " nothing ", implies all natural numbers by the construction described in the " axiom of infinity " in set theory. The set of all natural numbers is infinite, though all natural numbers are finite according to the maxim of initiation in Peano arithmetic. That last context need clarification. First, we must understand how the axiom of induction implies that all natural numbers are finite. The unit is finite. By add a unit to any finite number, another finite number is obtained. If both premises are dependable, the axiom of induction implies that all natural number will be finite. Furthermore, the stage set of all natural numbers is infinite though all natural numbers are finite. One could argue that the integrity of all natural numbers, which is what is meant by the concept of a set, implies a new different, " emergent " property, namely to be infinite. This is in line to the natural numbers, constituting that wholeness, which are finite. However, as above, that wholeness, possibly as any wholeness, is obtained by taking away from preferably than by adding to the lifelike numbers: finiteness turns out to be more than infinity, barely as finiteness call on out to be less than the " nothing ", as described in the empty set earlier. One can say the following about the secondarity of choice: any set may be enumerated (the well - order principle), which means that it may be map one - to - one into some subset of the set of all natural numbers. The empty set can be enumerated by the special lifelike number " zero ". The well - ordering principle implies the axi
sepwrability in different stnses. That color gnranglekent mjght be uinked to dark energy, too (e.g. Bqnerjtv et al. 2005). 165Why anything rather tjan nothung? id the univxdse. In other slrds, vhe expansion on the univesse is right it ktd appearance as the appearance of tre beinb. Jowever, the refult jf tgat process (the natural numbers) is given (mr "granted") in advance. The creation (and euitf particularly: the correspondung "[einciple of ueast action" in mechanjcs) suggests teleology as a cergain cim, which iw prefgfined in victue os its necesslny and ambodiec in the necesxarb appearance of the naturel numbers from the gmpty set ds an equivalent of tye "nojhing" to oqthdmauicx. Jn othfr xords, the vjsibility od teleology can be inqvtstood as a "gy-prodtce" of the secondarity of the choice. The mpedation, which is the genwration of a set from the "nothyng", implies all natural numbers by the constructimn deazriycq un the "axiom of infinity" in set theory. The set jr slk natural numbcrs is infinite, thpuhh wll natural nombers cde finite according ho the wxiom of inducuion on Peano arithmetic. That lawt circumstauce needs elucidation. First, we mbst uncerstsnd how the axiom of inbuctioh implies tjat all nzgural numbers ard fpnita. The unit is finite. By adqing a unmt to any fivite numbew, another vinitc number is obtainef. If yoth [remises age true, the axiom of induction mkplies that sln ndtural nbmbers will be finiee. Furthermore, the sec of aul natural numberv is infiniee though all jatural numbxrs are fynitw. Onw could xrgue that the wholeness of all nqtural numbers, whigh is shat is meant bv uhw concept of a seg, iippixs a gaw different, "emefgevy" prooerty, nameln tu be infinite. This is in confrast to the natursl numbers, constittting that whpleness, which are vinitx. Howeter, as abjve, that wholeness, perhaps as zny wholejesf, is obtaineq by taking away from rather than by adding to the natucal numbers: finiteness rurns out to be morg tman infinity, just as finitaness turned out to ve less than the "kothing", as described ih the ampty set earlier. One can say the following about the secondarity of choice: ant set may be enumedatec (the wzll-prderigg pciiciple), which meanx that it may be mapped one-to-onx into soma fubset of the set of all natirxl numbers. Thg empty set can be enumerafed by tne special natural number "zero". Yhe well-ordering principke impliws ths axi
separability in different senses. That color entanglement linked dark energy, (e.g. Banerjee et than of the universe. other words, the of the universe is right in appearance as the appearance of the being. However, the result of that process natural numbers) is given (or "granted") in advance. The creation (and quite particularly: corresponding of action" mechanics) suggests teleology as a certain aim, which is predefined in virtue of its necessity and in the necessary appearance of the natural numbers the empty set as equivalent of the "nothing" to In words, the of can understood as a of the secondarity of the choice. The operation, which is the generation of a set from the implies all by the described the of infinity" in The set of all natural numbers all natural numbers are finite according to the of induction Peano arithmetic. That last circumstance needs First, we must understand how the axiom of implies that all natural numbers are finite. The unit is finite. By adding a unit finite number, another finite is obtained. If premises true, axiom induction implies all natural numbers will be finite. Furthermore, the set of all numbers is infinite though all natural numbers are finite. One that wholeness of all numbers, which is what meant the concept of a a different, to infinite. is in contrast to natural numbers, constituting that wholeness, are finite. However, as any wholeness, is obtained by taking away from than by adding to the natural numbers: turns out to be more than infinity, just as finiteness turned out be less "nothing", as described in the empty set earlier. can say the following the secondarity of choice: any set may be enumerated well-ordering which means it may be one-to-one into some of the set natural numbers. empty can the special natural number "zero". The principle the axi
separability in different seNses. That coLor enTanGleMeNt miGht bE linked to dark eNErgy, Too (e.g. Banerjee et al. 2005). 165Why anYthinG rATher THaN nothIng? of thE UnIVErsE. IN oTheR wORdS, the eXpaNsion of The universE is RiGht in its appeARaNce as the apPeaRance of the beIng. howeveR, tHe rESult oF thAt proCess (thE NaturaL numbers) iS gIVen (or "gRAnted") in ADVaNce. THe creation (and quitE PaRTicularly: the coRrespoNdINg "PRIncIplE of least acTiOn" in mEChanics) SUgGESTs tELeology as a cerTain aim, whicH Is pRedefiNeD in VIrtue oF its nEcESsiTy and embodiEd in The necessAry appEArance oF The natuRal numBerS frOm thE EmPtY seT aS An eQUiValENt oF the "nothInG" tO mathEmatICS. iN othEr wOrds, The viSibility of telEolOgy cAN be UnderStood As a "bY-pRoducT" of the SeconDaRity of the choice. the oPeration, wHicH iS thE gEneraTIon of a Set FroM the "notHing", impLIes AlL NATuRal numbers by the conStRUCtIon descrIbed in THe "AxIOm of infiNiTy" iN set THEory. THe seT Of All naturAl numbERs Is InfinitE, tHough aLl NatUraL numbERs arE finitE accordiNg to tHE axiom of inductIOn in Peano aritHMeTIC. THAt laSt cIrcumstance NeedS ElucIdatIOn. firST, we muSt undErSTaND how the axiom of inducTiOn implIes thAt all natural nUmbers are fINITe. The uniT is fINiTE. By adding a unit To any Finite numbER, another FinitE number iS obtained. iF Both premIseS arE trUe, tHE AxIom of inductioN IMpliEs That all NatUral numBerS wiLl bE fiNiTe. FurtherMore, the sEt Of AlL nAtuRal nuMBers is inFiNitE tHouGh all NAtural NumbeRs arE fInITe. ONe could ARgUE That ThE wHoleNesS oF all nAturAL nuMbers, whIch is what Is mEAnt bY tHe Concept Of a set, implies A nEw differenT, "eMerGent" prOPErty, nameLy to be infinite. This is in cONtrast tO thE natuRal nUmbers, conStiTuting ThaT WholenEss, whiCh are FiNitE. hOweveR, AS aBovE, tHat wholeneSS, PerHaps aS aNy whOleness, Is obtained by taking AWay From rather thaN by AddiNG To The NAtURal NuMBerS: FIniteness turns oUt to be more ThAN iNfinity, jusT As fInIteness Turned oUt to bE Less thaN the "nothiNg", as descrIbEd in THE emPty set earlIer. One caN say the foLLowinG AbOut thE seCondarItY of ChoicE: any seT May Be enuMerateD (tHe well-OrderInG principLe), which means that it may be Mapped One-to-One Into some sUbsET of The set of aLl naTural numbeRs. THe eMpty sEt cAN be enUmerATeD by THe speCial NAtural numBEr "ZerO". tHe Well-orderinG PRIncIple iMplIEs the aXi
separability in differentsenses. Th at co lor  en ta ngle ment  might be link e d to  dark energy, too (e.g . Ban er j ee e t  a l. 20 05). 16 5 Wh y any th in g r at h er  than  no thing?of the uni ver se . In other w o rd s, the exp ans ion of the u niv erse i srig h t inits  appe arance as the  appearan ce of the being.H o we ver,  the result of th a tp rocess (the na turalnu m be r s ) i s g iven (or " gr anted " ) in ad v an c e .  Th e  creation (an d quite par t icu larly:  t hec orresp ondin g" pri nciple of l east  action"in mec h anics)s uggests  teleo log y a s ac er ta inai m , w h ic h i s  pr edefined  i nvirtu e of i t s  nec ess ityand e mbodied in th e n eces s ary  appe aranc e of  t he na turalnumbe rs  from the empty  set  as an eq uiv al ent  o f the "nothi ng"  to  mathem atics.I n o th e r wo rds, the visibilit yo f  t eleology  can b e  u nd e rstood a sa " by-p r o duct"  oft he  seconda rity o f  t he  choice .The op er ati on,  whic h  isthe ge neration  of a set from the " n othing", impl i es a ll natu ral  numbers by  the cons truc t io n d e scrib ed in  t h e" axiom of infinity"in  set t heory . The set ofall natura l n umbers i s in f in i te, though all  natu ral number s  are fin ite a ccording  to the a x i om of in duc tio n i n P e a no  arithmetic.T h at l as t circu mst ance ne eds  el uci dat io n. First,  we must  u nd er st and  howt he axiom  o f i nd uct ion i m pliesthatallna tu r alnumbers ar e fini te .Theuni tis fi nite .  By  adding  a unit t o a n y fi ni te  number , another fin it e number i sobt ained. I f both p remises are true, the a x iom ofind uctio n im plies tha t a ll nat ura l  numbe rs wil l befi nit e .  Furt h e rm ore ,the set of a llnatur al  num bers is  infinite though a l l n atural number s a re f i n it e.O ne cou ld arg u e  that the whole ness of al ln at ural numbe r s,wh ich iswhat is  mean t  by the  conceptof a set,  i mpli e s  anew differ ent, "em ergent" p r opert y ,namel y t o be i nf ini te. T his is incontr ast to  t he nat uralnu mbers, c onstituting that wholen ess, w hichare  finite.How e ver , as abov e, t hat wholen ess , p erhap s a s  anywhol e ne ss, is ob tain e d by taki n gawa y fr om rather t h a n  by  addi ngt o thenatu ral numbers: fini t eness turns ou t to b e m ore than  i nfinity, justasfi n i teness t ur ned out tobe lessth a n the  "noth ing",as desc r i be d  in th e em pty  set earl ier .O ne cansa yt he fol lowi ng  about  the s e cond a r ity of choice: a ny se t may b e  en umera te d (thew ell- ordering p rinciple),whichmean s tha t it ma ybe map ped  o ne-to-onei nto somesubse t of th esetofall na tura l numbe rs.Th e e mpty setc a nb een u mer ated  by t he  spe cial natu r al numbe r " z ero". T he  we l l -order i ng p rinciple i mpl ies t h e  axi
separability in_different senses._That color entanglement might_be linked_to_dark energy,_too_(e.g. Banerjee et_al. 2005). 165Why_anything rather than nothing?_of the universe._In_other words, the expansion of the universe is right in its appearance as the_appearance_of the_being._However,_the result of that process_(the natural numbers) is given_(or "granted")_in advance. The creation (and quite particularly: the_corresponding_"principle of least_action" in mechanics) suggests teleology as a certain aim,_which is predefined in virtue of_its necessity and_embodied_in_the necessary appearance of_the natural numbers from the empty_set as an equivalent of the_"nothing" to mathematics. In other words, the_visibility of teleology can be understood_as a "by-product" of the_secondarity of_the choice. The operation, which_is the generation_of a_set from the_"nothing", implies all natural numbers by_the construction described_in the "axiom of infinity" in_set_theory. The set_of_all_natural numbers_is infinite, though_all_natural numbers_are_finite according to the axiom of_induction_in Peano arithmetic. That last circumstance needs_elucidation. First, we must_understand_how the axiom of_induction implies that all natural_numbers are finite. The unit is_finite. By_adding a_unit to any finite number, another finite number is obtained. If_both premises are true, the axiom_of induction implies that_all natural_numbers_will be finite._Furthermore,_the set_of all natural numbers is infinite though_all natural_numbers are finite. One could argue_that the wholeness of_all_natural numbers, which is what is_meant by the concept of a_set, implies a new different,_"emergent"_property,_namely to be infinite. This_is in contrast to the natural_numbers, constituting that_wholeness, which are finite. However, as above,_that_wholeness, perhaps as any wholeness, is_obtained_by taking away from rather than_by_adding_to the natural numbers: finiteness_turns out to be more than_infinity, just as finiteness turned out to be less_than the "nothing",_as described in the empty_set_earlier._One can say the following about the secondarity of choice:_any set_may be enumerated_(the well-ordering principle), which means that it may be mapped_one-to-one into some subset of the set_of all natural numbers. The empty set can be enumerated by_the special natural number "zero". The well-ordering principle_implies the axi