I have two small questions:

1 - In the appealing flight analogy:
>We can think of the arrows in our Hasse diagrams as _one-way streets_ in two cities, \$$X\$$ and \$$Y\$$. And we can think of the blue dashed arrows as _one-way plane flights_ from cities in \$$X\$$ to cities in \$$Y\$$. Then \$$\Phi(x,y) = \text{true}\$$ if we can get from \$$x \in X\$$ to \$$y \in Y\$$ _using any combination of streets and plane flights!_

Should "from cities in \$$X\$$ to cities in \$$Y\$$" be "from streets in \$$X\$$ to streets in \$$Y\$$" instead (as \$$X,Y\$$ are already cities themselves)?

2 - In **Puzzle 174**:
>**Puzzle 174.** Suppose \$$g: Y \to X \$$ is a monotone function from \$$X\$$ to \$$Y\$$...

Should this be a function from \$$Y\$$ to \$$X\$$ instead?