Fix a few typos in type inference chapter

Also try to test the top example

Author: jonas-schievink

src/type-inference.md

@@ -6,14 +6,14 @@ expression.
 It is what allows Rust to work with fewer or no type annotations,
 making things easier for users:
 
-```rust,ignore
+```rust
 fn main() {
     let mut things = vec![];
-    things.push("thing")
+    things.push("thing");
 }
 ```
 
-Here, the type of `things` is *inferenced* to be `&str` because that's the value
+Here, the type of `things` is *inferred* to be `Vec<&str>` because of the value
 we push into `things`.
 
 The type inference is based on the standard Hindley-Milner (HM) type inference