If you look at the Unicode Block for Mathematical Alphanumeric Symbols you notice that the MATHEMATICAL DOUBLE-STRUCK CAPITAL C is missing. And it is not the only one. Why? What is the point of having DOUBLE-STRUCK if you don't have all 26?
The code chart (PDF) for Mathematical Alphanumeric Symbols contains the following explanation:
Double-struck symbols already encoded in the Letterlike
Symbols block and omitted here to avoid duplicate encoding.
Here “and” is apparently to be read as “are”. Anyway, the point is that the Letterlike Symbols block already contains the double-struck C (as well as a few other double-struck letters). This reflects their relatively common use in mathematics (e.g. for ℂ the use as an alternative to C to denote the set of complex numbers) and their presence in old character codes. The block does not have enough code points for adding all the double-struck letters, so additions were made elsewhere. To keep the allocation natural, holes (reserved code points) were left there.
The code chart contains cross references to the characters allocated elsewhere, e.g. for the reserved code point 1D53A is has the comment “→ 2102 ℂ double-struck capital c”.
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