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Topic: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR:
THE REALS ARE UNCOUNTABLE!

Replies: 47   Last Post: Jan 12, 2013 11:33 AM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF CANTOR: THE REALS ARE UNCOUNTABLE!
Posted: Jan 10, 2013 3:20 AM

In article
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:

> Cnsdr thn th dffrnc btwn th fnnl nd th sv. n
> mght pr th md nt th fnnl nd dffrntt ch s th
> fll t, nd th fnnl wld fll,  smpl rt prblm. Th sv
> thn mght smply dffrntt crss t nc, v th strctr
> bng tslf dfnd n th prlll: nstd f brngng ch tm
> t th dstngshmnt,  swp thrgh thm dffrntts thm t
> nc.
>
> l Jfr,  pprct tht y fnd prfndty n th ncntblty
> f th rglr, wll-fndd pwrst f th rglr, wll-fndd
> nfnt st, yt s wll y knw f dvlpmnt wth nfnt
> lmnts n th nfnt st f fnt thngs, r f th nt-
> fndtnl, r xprssly f hw tdy's thrsts grppl wth th
> mst fndmntlly lrg, th nvrs r th ttlty f rdnls,
> whch r dffrnttd v thr strctr mr strngly thn
> xtnsnlty. Y knw tht xtnsnlty nd fr tht mttr th
> prtclr xmtztn f nfnty s rglr nd wll-fndd,
> rstrctd, s jst tht: n ssrtn f n bstrct thng. Crtsy
> th lck f nvrsl qntfctn vr th ndctvly fllwng
> lmnts, t s knwn tht thry s thr ncmplt, r
> ncnsstnt. t bst cnsstnt, thr r pln tr fcts bt
> ts bjcts tht rn't f ts thrms, bt th strctr f ch s
> dclrd.
>
> Rssll, fr xmpl, ntd tht th st f ll sts tht dn't
> cntn thmslvs, wld cntn tslf. Tht's smpl: t ds.
> nd, tht's ZF's nvrs.
>
> S, whl n th n hnd t mks sns tht y stt yr blf n
> th vldty f th ncntbl, f sd thry's xms nd ts
> mmdtly ccssbl thrms crtsy xtnsnlty nd 
> prtclrly dclrd rstrctdly rglr nfnty, bcs y
> dscrb thrs gnrlly nd fl t rsnbl t xprss t yr
> dnc yr blf drctly, s wll thr r smply thrs
> wtht ths xms nd y wll knw tht.
>
> Thn, wth rgrds t ttmpts t ndrstnd nd rgrsly dfn
> mthmtcl bstrctns f th cntnm, f nmbrs, nd gmtry,
> nd smply cllctns r grpng nd sprtn, bvsly ngh
> vryn gs bt tht s prt f rsn. Thn wth rgrds t tht
> "nly fnts mk n nfnt" bt thn "nfnts dn't mk n
> nfnt", t's nt ncssrly ll-cncvd t fnd ltrnt
> xms, r prtclrly  lck thrf, s dffrnt tr rslts,
> thn t th ndrstndng nd dstnctn f mthmtcl
> bstrctns.
>
> Thn, whr 'm prtclrly ggrssv nd nstd f smply dfnng
> strctrs n vc, bcs thy'r nt, nstd crry frwrd th
> gnrl cs f wrkng twrd thr cncltn, f th nvrsl
> nd mpty,  g bt tht cnstrctvly, fr mthmtcs fr
> hmnty nd nt jst mthmtcns fr thmslvs: fr th ppld.
>
> Th nvrs s st s ts wn pwrst.  fnd t sr t blv
> tht th ll xsts, thn tht t dsn't.
>
> Bcs, thrws, t wldn't.
>
> Rgrds,
>
> Rss Fnlysn

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