[Tistron]

You're saying that 0.999...=1, and simultaneously you are saying that 3 × 0.333... = 1 and not 0.999...

What? How can it be that a=b and a≠c when b=c?

[tsimionescu]

I'm saying that, in the hyperreals as well as the reals, I am 100% certain that 3 × 0.33... = 1. I am not as sure that 0.999 = 1 with the hyperreals, BUT, if it's true as the author claims that 0.99... ≠ 1 in the hyperreals, then it must follow that 3 × 0.33... ≠ 0.99... in the hyperreals.