For those who might wonder where the error >>28 is but do not wish to engage, the step from "1*(1/10)*(1/10)*(1/10)*...=0" to "1=0/(1/10)/(1/10)/(1/10)/..." repeats the same fallacy >>27 because "1*(1/10)*(1/10)*(1/10)*..." is lim[n->inf](1/10)^n and there is no real number that you can multiply it with to ever get 1 back.
As for the archimedean trolling, you can dismiss it entirely. The proof is quite simple. If a field is ordered and is non-archimedean then it is incomplete, but R is both ordered and complete, thus R is archimedean. The other proof that was posted >>31 >>33 is also valid.