From the TOC, it looks like an elementary algebra book.
Students usually don't see rigorous construction of integers and rationals till classes titled something to the effect of "intro to proofs 101", "intro to discrete analysis", "abstract algebra 101", "elementary general algebra", "elementary set theory", "basics of elementary number theory"... And the construction of reals would have to wait till something like "elementary real analysis 101".
Usually, after elementary algebra come 3 semesters of calculus. Subject as vague and, uhh, as un-mathematical as it contains neither concrete definitions(other than the one for derivative), nor any theorems. Nothing substantial to grasp at when drowning.
Traditionally, actual learnable definition-lemma-theorem-corollary-examples style math starts after the calculus sequence. So the audience for the linked book is at least 2 classes removed from the time they get to see number construction.
While elementary algebra is both useful and unavoidable, I don't think the same about the calculus. IMHO, the latter is just a waste of time.
The sequence elementary algebra -> intro to math proofs -> elementary real analysis -> Lebesgue Integral by way of Daniell-Riesz -> complex analysis -> non-Euclidean/abstract topology -> measure theory -> probability theory -> differential geometry would give anyone world- class education into the nature of functions which the calculus sequence is kind-sorta supposed to give you a tiny and very distant taste of.
Students usually don't see rigorous construction of integers and rationals till classes titled something to the effect of "intro to proofs 101", "intro to discrete analysis", "abstract algebra 101", "elementary general algebra", "elementary set theory", "basics of elementary number theory"... And the construction of reals would have to wait till something like "elementary real analysis 101".
Usually, after elementary algebra come 3 semesters of calculus. Subject as vague and, uhh, as un-mathematical as it contains neither concrete definitions(other than the one for derivative), nor any theorems. Nothing substantial to grasp at when drowning.
Traditionally, actual learnable definition-lemma-theorem-corollary-examples style math starts after the calculus sequence. So the audience for the linked book is at least 2 classes removed from the time they get to see number construction.
While elementary algebra is both useful and unavoidable, I don't think the same about the calculus. IMHO, the latter is just a waste of time.
The sequence elementary algebra -> intro to math proofs -> elementary real analysis -> Lebesgue Integral by way of Daniell-Riesz -> complex analysis -> non-Euclidean/abstract topology -> measure theory -> probability theory -> differential geometry would give anyone world- class education into the nature of functions which the calculus sequence is kind-sorta supposed to give you a tiny and very distant taste of.