fdhner

Naq fb ba - gurer vf nyjnlf n arkg ebj bs fdhnerf, nf gur fznyyrf fdhner va gur ebj pna abg gbhpu gur obggbz fvqr bs gur havg fdhner.

Gurer unf gb or n fznyyrfg fdhner F3 nzbat gurz jvgu fvqr yratgu < 0.5*0.25 = cbjre(0.5,3).

Gurer unf gb or n fznyyrfg fdhner nzbat gurz, jvgu yratgu < 0.5* fvqr_yratgu_bs(F1) = 0.25.

Vzntvar n frg pbagnvavat sbhe naq artngvir sbhe naq lbh znc `fdhner` bire vg… Gur fvmr bs gur pbyyrpgvba jbhyq punatr!

Gur fznyyrfg fdhner nzbat gurz unf n fvqr yratgu < 0.5, yrg'f pnyy vg F1.

My informal counter proof by contradiction (decrypt with rot13.com): fvapr gur cnegvgvba vf svavgr, gurer vf n fdhner Z jvgu gur fubegrfg fvqr.

Abj pbafvqre gur fdhnerf nybat gur gbc fvqr bs gur havg fdhner.

Abj pbafvqre gur ebj bs fdhnerf ng gur obggbz bs gung fdhner.

Urapr V pna tb ba yvxr gung vasvavgryl, orpnhfr yvz cbj(0.5,a) = 0 riraghnyyl V'yy svaq n fdhner gung vf fznyyre guna Z, pbagenqvpgvba.

Begubtencuvp cebwrpgvba nybat gur yvar pbaarpgvat nal rqtr zvqcbvag gb gur bccbfvgr rqtr zvqcbvag tvirf n fdhner, lvryqvat 3 fhpu cebwrpgvbaf (cyhf gurve bccbfvgr pbhagrecnegf).