\Bbb is deprecated in LaTeX (where it is provided by the package amsfonts).
I used that wording because, at least in my professional circle, "TeX" is used nowadays as a generic term to denote "TeX with one of its commonly used macro packages, typically LaTeX". I am aware that it is not accurate, but it's the common use. It's a bit like "sellotape", "xerox" or "Linux".
]]>Also, you seem to be confusing TeX (a program written by Knuth) and Plain TeX (a macro package for TeX, just like AMS TeX and LaTeX).
]]>In addition to mathbb, many use mathbf (boldface). I've even heard purists claim that blackboard bold should be reserved for blackboards.
If you want to emulate some of the old Springer lecture notes, you can superimpose two Cs or mush a C and an I together using negative spaces.
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