> So do you claim that d is not in the list but all its finite initial > segments (d_1, ..., d_n) are in the list?
YES . Finally .
> If so, what is the >difference > d \ U(d_1, ..., d_n) > d and (d_1, ..., d_n) understood as sets of nodes of paths in decimal > tree.
The tree is irrelevant unless you can do a small-step STEP by STEP proof , using LOGICALLY VALID of how it's relevant and how it relates to the LIST . Cantor's argument was all about the LIST ,not some made- up tree .