>>28
The interesting thing is that such a number as .9(...)9, if it even exists, doesn't belong to the set of reals. While .9... (where .9... is .9 repeating) most certainly does.
>>15, >>25 should read
>>6's link more thoroughly. This is discussed there in great detail.
>>15, >>25
There is no "infinitesimal" difference between .9... and 1. Check the linked post for Icarus' Misconception 8 (That "There is a least number greater than or greatest number less than a given real number.") Your view seems to be centered on this misconception. 0.9... is not, and cannot be, the "greatest number that's less than" 1.