So, Friday in class, my teacher was talking about how .99999... = 1.00000..... So, this makes sense and all, but this is my question: How do you know that 1.230000... = 1.230000....? I guess that my real question is that if a1.a2a3a4...aN = d1.d2d3d4...bN (finite number of digits) then all the corresponding digits are the same. I thought that this was true, but then again, I thought .999... < 1.000. So. Is it true? Is it provable in the same way .999... = 1? If so, what is it?