Puzzle 75 is about things like this "a dozen eggs costs more than a stick of butter". We have a set \$$\mathbb{R}\$$ whose elements are _amounts of money_, ordered in the usual way. We have a set \$$X\$$ whose elements are _things you can buy in the grocery store_. And we have a function \$$f: X \to \mathbb{R}\$$ mapping each thing you can buy in the grocery store to its price. Say

$f(\text{a dozen eggs}) = 3.50$

and

$f(\text{a stick of butter}) = 0.75$

Then we say

$\text{a stick of butter} \le_X \text{a dozen eggs}$

because

$0.75 \le_{\mathbb{R}} 3.50 .$

This is just a way of saying that a stick of butter is cheaper than a dozen eggs. It makes perfect sense. Please, someone do these puzzles!

By the way, Brandon passed his thesis defense, and all my students are happy. =D> =D> =D> =D> =D> =D>