peter.hilton (233) [Avatar] Offline
#1
The notation choice in chapter 2 is tricky, because you're mixing mathematical and programming function notation. In DDD terms, set theory and the Java programming language are two different bounded contexts. This is tricky because there might not be a good solution, but it’s worth mentioning and trying to be consistent.

Perhaps this is worth a sidebar or a table to compare and separate mathematical and Java notation for functions: function names, parameters, types, inverse, etc.

For example, section 2.1.1.2 (Inverse functions) mentions ‘the set of signed integers (positive and negative, noted as Z)’. It would be helpful to be clear that this is mathematical language, and to use the right symbol ('fat' Z with a double stroke), and perhaps to note that 'the set of integers' (mathematics) corresponds to the concept of the Java Integer type.

Similarly, section 2.1.1.5 (Functions of several arguments) mentions 'N x N'. It would be helpful to mention that this is the cross product of two sets, and say what this means (handle or declare). Also, the lowercase 'x' should be a multiplication sign '×'.
Pierre-Yves Saumont (181) [Avatar] Offline
#2
You're certainly right about the notation. The problem is that the production process is different for the meap than for the final book. I have to check if there is a way to use mathematical characters in the manuscript.

Regarding additional explanations regarding mathematical and Java notation, it would definitely be a plus. I will come back to this as soon as I have finished writing the last chapters.
peter.hilton (233) [Avatar] Offline
#3
Sounds good.

Given the occasional stray back ticks, I’m guessing that your tool chain is Markdown to DocBook, in which case you're probably okay with single Unicode characters, like the multiplication sign.
212920 (3) [Avatar] Offline
#4
Chapter 2, page 18 , section "WHAT MAKES A RELATION BETWEEN TWO SETS A FUNCTION"

5 math implications are mentioned.

1: There cannot exist elements in the domain with no corresponding value in the
codomain.
2: There cannot exist two elements in the codomain corresponding to the same
element of the domain.
3: There may be elements in the codomain with no corresponding element in the
source set.
4: There may be elements in the codomain with more than one corresponding
element in the source set.
5: The set of elements of the codomain that have a corresponding element in the
domain is called the image of the function.

Need your help to understand if and how #2 and #4 co-exist.. tried to fit this in case of function and inverse function both, not sure if i understood the expected meaning here, kindly advise.
Pierre-Yves Saumont (181) [Avatar] Offline
#5
Think of functions square and square root for real numbers. square(2) and square(-2) both correspond to 4. No real number has two square values. This is a function.

Now consider square_root with positive real numbers as its domain. This is not a function because square_root(n) has two values (one positive and one negative).