Small fixups

src/ch01-00-forward.md

@@ -13,9 +13,9 @@ provide a more recent account of nix with more of a focus on giving the user
 intuition around what nix is doing rather than a deep understanding like nix-pills.
 
 The goal is not to replace any existing nix guides or documentation, but rather
-provide a good starting place for new users. Much of the motivation for writing
-this is to provide a "nix equilavent of the [rust-lang book](https://doc.rust-lang.org/book/)",
-where there is one resource, which can be read end-to-end in an after,
+provide a good starting place for new users. Motivation for writing
+this is to provide a "nix equilavent of the [rust-lang book](https://doc.rust-lang.org/book/)".
+Where there is one resource which can be read end-to-end in an afternoon and
 able to equip the reader with the knowledge necessary
 to thrive in the nix ecosystem.
 

src/ch02-00-introduction.md

@@ -2,11 +2,11 @@
 
 # The Nix Package Manager
 
-The Nix is a package manager which focuses on
+Nix is a package manager which focuses on
 caputuring all inputs which contribute to building software.
 The result of factoring all of the information about building
 the software is called a derivation. This aggregated information includes where
-the source code is pull, configuration flags, patches,
+the source code is pulled, configuration flags, patches,
 dependencies, build steps, installation steps, and many other potential inputs.
 
 This information is aggregated through hashing, and allows nix to
@@ -21,17 +21,14 @@ a single variant of a piece of software.
 
 There's roughly four layers of abstractions in the official nix ecosystem, these are:
 
-- Nix(-lang)* - The nix language
+- Nix - The domain-specifc language used to write nix expressions
 - Nix - The package manager
 - Nixpkgs - The package repository
 - NixOS - A linux distribution built upon nixpkgs
 
 All of these topic will be discussed in greater detail in later sections, but a 
 quick summary is provided below.
 
-*: Generally the distinction between the nix language and package manager is done
-by context.
-
 ## The Nix Language
 
 The Nix language is a Domain-Specific Language (DSL) which is designed to