Java charAt used with characters that have two code units

It sounds like tho book is saying that 'ℤ' is not a UTF-16 character in the basic multilingual plane, but in fact it is.

Java uses UTF-16 with surrogate pairs for characters that are not in the basic multilingual plane. Since 'ℤ' (0x2124) is in the basic multilingual plane it is represented by a single code unit. In your example sentence.charAt(0) will return 'ℤ', and sentence.charAt(1) will return ' '.

A character represented by surrogate pairs has two code units making up the character. sentence.charAt(0) would return the first code unit, and sentence.charAt(1) would return the second code unit.

See http://docs.oracle.com/javase/6/docs/api/java/lang/String.html:

A String represents a string in the UTF-16 format in which supplementary characters are represented by surrogate pairs (see the section Unicode Character Representations in the Character class for more information). Index values refer to char code units, so a supplementary character uses two positions in a String.

According to the documentation String is represented internally as utf-16, so charAt() is giving you two code points. If you are interested in seeing the individual code points you can use this code (from this answer):

final int length = sentence.length();
for (int offset = 0; offset < length; ) {
   final int codepoint = sentence.codePointAt(offset);

   // do something with the codepoint

   offset += Character.charCount(codepoint);
}