# Is there a resource about integer constructions and motivations?

I have an assignment about the foundations of mathematics.

I am trying to compile a list where I get common construction of integers and a small writing about the constructor and their explanation.

For example, I have the ordered pair construction by Dedekind, and his explanation via his principle of “generality”, where he writes that definitions appearing in a restricted form can be extended to avoid arbitrariness.

What about the original constructors of other constructions, where can I read about their commentaries?

• E.Bloch, The Real Numbers and Real Analysis and F.Waismann, Introduction to Mathematical Thinking Mar 5 at 11:12
• The ordered pair construction is for rational numbers, not integers. Mar 5 at 12:14
• There is also an ordered pair construction of integers from natural numbers Mar 5 at 19:19
• @MauroALLEGRANZA in “introduction to mathematical thinking” I was reading the chapter on construction of integers and the author mentions a hueristic principle “principle of permanence of forms” and says mathematicians want to preserve existing structure as much as possible. Is this still true? How do I know I’m not reading stuff that is outdated printed in 1952 Mar 6 at 4:45
• @Conifold ... Sometimes we construct $\mathbb Z$ by taking ordered pairs in $\mathbb N$ with equivalence relation $(x,y) \sim (u,v) \Longleftrightarrow x+v = u+y$ Mar 6 at 18:24