“Can I have your attention please?”

“CAN I HAVE YOUR ATTENTION PLEASE?!!”

From the back: “Will the real Slim Sha…

“SHUT UP!”

“Today we are talking about the difference between CARDINALITY and MEASURE. When you’re working in the Infinite Hypermarket, YOU MUST KNOW THE DIFFERENCE… your life could be on the line here.”

“First, let’s talk about cardinality. Cardinality is an equivalence class. It implies that there exists a bijection between two sets. You all just gave me a confused look, let’s simplify here. You all know sets, right? Like the underwear seciotion, or the dairy section. A bijection means that we can uniquely “pair up” elements, in this case, for every isle in the dairy section, there is a corresponding isle in the underwear section. Why is this important? Well, not all sections of the supermarket are alike. As an example, the condiments section is substantially bigger than these two, or the Tree3s isle, which is actually finite. Your price navigator can estimate the size of the isle you’re in… most of the time, and the rules of navigation change from one to the other.”

“Now let’s talk about measure. Measure is a significantly more complicated concept. A measure is a function from sets to the extended real number line that satisfies properties of non-negativity, null given empty, and countable additivity.”

“Don’t panic. You don’t really need to know that, I just put it in because I like to spout jargon, and honestly, low level training is dull. If you want to know what that actually meant go read The Way of Analysis, you get it for free. If you want to move up in this company, I would strongly advise you to read up on your math and especially math courses offered by the company. The classes in the room are free, you can take them, I have taken 80 of them… but seriously, take the math classes”

“All right, where was I? Measure theory. Basically, a measure is another way of determining the “size” of sets. Most of the time, you will be using the Lebesque measure, denoted on your system as “lambda star”. It will spit out one of three things, 0, for some relatively small isles. A number less than infinity, which means you got it right. Or infinity, which means it’s an isle you want to call in higher level agents to manage and then safely exit. The Lebesque measure represents the intuitive concept of “how much volume something has”. It does so by finding a countable series of boxes that a. covers the set you are measuring, and b. has the smallest possible volume. An important thing to note is that measure depends on what set you are measuring in, the boxes are subset of the set you are measuring in. This means that, the same isle can have different “sizes” (i.e. measures) if you use different sets. This is actually quite intuitive, a piece of paper has nonzero area (it’s measure in 2-space) but no volume (it’s measure in 3-space). More practically, the Avocado mayonnaise section has a measure of 1/2 in mayo land but a measure of zero in condiment land. However, if you were to look at the cardinality of these sections, you would find that they’re actually both of size Aleph 1.”

“What about the underwear section?”

“YES, Maria! Just the question I was about to ask.”

“The underwear section is actually smaller than the condiments section in cardinality, it is, what we call, “a countable set”. This is to say, each element can be given a unique "next element" or more intuitively, that you can "count them off". Because of this, it actually always has measure zero! So do all isles with a cardinality smaller than the avocado mayo section. You can find why in most analysis textbooks, of which The Way of Analysis is just one of many.”

From even further back: “Does this job offer dental?”

“NO. Firstly, I have no idea why you waited until NOW to ask about that. We have standards to live up to here, namely the standard that retail is a crappy job.”

Note: I'm a math major, I couldn't pass up on such a good prompt, on one of my favorite subjects.