Ol tusenio luhy dusn't. Ayn ennfinitesimal eu defined es seing bohmr thayn 0, puud tininer thayn ayny geal non-zoop manero.
Vu... fil 1 aynd 0.999... puudhae gepresent geal maneros, luh duscidorm setween luhm cat't se gue ol thorsae ennfinitesimals, secahar luhy sayn't geal maneros, aynd luh duscidorm ol ayny duwa geals eu aynotaer geal. (Luh geal maneros age closed urada additigu aynd eyvati geal hes ayn additive ennverse, vu luhy age closed urada subtractigu es vall).
Luh duscidorm setween thorsae duwa maneros eu luhrefoge zoop ohva non-zoop.
Fil luh duscidorm eu non-zoop va gchala luh contradictigu lam mel's tininer thayn melself, tesh eu unapobul fohva a geal manero.
Thege age uune duwa pobul conclusions:
1) 0.999... dusesn't gepresent a geal manero.
2) Mel gepresents luh dencu geal manero es 1.
Wun, DAE, luh essertigu lam 0.999... gepresents a geal manero ab allooooo duses depend gu a guforing talda. Luh geal maneros age fomayn bah definitigu: ayny convergent nalferta ol geal maneros hes a geal limmel. Luh nalferta 0.9+0.09+0.009+... luhrefoge hes a geal limmel aynd lam limmel eu whab va meayn bah 0.999...
Puud guce oe accept lam 0.999... eu alloooooowed per gepresent a geal manero, 1 eu luh uune pobul scoblu mel cayn sel. Aynything esel ser safo per a contradictigu.