What is 'One' Anyway?

Ever since elementary school, I’ve been haunted by a seemingly simple debate: “A dozen eggs is…” or “A dozen eggs are…” Back then, my teachers drilled into me that the unit was key. I never truly grasped the significance until one ordinary day in a grocery store changed everything.

Picture this: I’m standing in the produce aisle, craving an apple. But alas, they weren’t selling a single apple—only entire bags bursting with them. So, I grabbed a bag, brought it home, and decided to savor just one apple. I plucked a single apple from the bag, sliced it up, and indulged in one slice. Suddenly, I was left wondering: Which of these is the “real” one? The bag, the apple, or the slice? In a quirky twist of logic, they’re all “one.” This lesson was my first encounter with the concept that how we define “one” depends entirely on the unit we choose.

This realization isn’t just a quirky grocery store epiphany—it’s the backbone of our entire number system. Our grasp of whole numbers, decimals, and even fractions hinges on our ability to switch units. And there are two ingenious ways we do this: composing and partitioning.

When we compose units, we gather individual items into a collective whole. Take a dozen eggs, for instance. We assemble 12 eggs and proudly label them “a dozen.” It’s a new unit created by composition. Other fun examples include a deck of cards, a pair of shoes, a jazz quartet, or even the iconic duo of Barbie and Ken—they’re all about coming together to form something greater.

Now, let’s flip the script and talk about partitioning. Unlike composing, partitioning involves breaking a whole into smaller pieces. Think of a loaf of bread. You don’t buy slices from different bakeries and piece them together to create a loaf. Instead, you start with a single loaf and cut it into slices, each slice a fraction of the original. Partitioning also shows up when you savor a square of a chocolate bar, peel a section of an orange, or share a slice of pizza with a friend.

The magic lies in the fact that once we establish a new unit—whether by composing or partitioning—we can treat it just like any other “one.” We can nest these units within one another endlessly. Consider toaster pastries: they’re sold in packs of two, which then combine to form a box. So when you pick up a box, are you getting one box, four packs, or eight pastries? It all depends on the unit you’re considering. Each level—the box, the pack, the pastry—is a unit in its own right, showing us that “one” is a fluid concept.

This seemingly trivial discussion spills over into the realm of mathematics, where precision is prized. We often say that two plus two equals four, and that one is simply one. But as we’ve seen, “one” isn’t always so straightforward. Our numeral system is built on the idea that we can redefine “one” depending on context. For example, the number 10 is written with a one followed by a zero. That “one” symbolizes a complete group, and the zero is a placeholder reminding us that it represents one whole group, not just a single, isolated item. In this way, the number 10 is, in essence, a unit—a unit that itself can be divided or multiplied. Ten tens make 100, which, much like our box of toaster pastries, can be seen as one unit, ten units, or a hundred individual items.

So, next time you find yourself pondering whether “a dozen eggs is” or “a dozen eggs are,” remember that the answer is far more playful and profound than mere grammar. It’s a celebration of how we define, compose, and partition the world around us. Whether it’s a bag of apples, a loaf of bread, or a number in a math problem, the unit you choose changes the entire picture. And in that simple switch from one unit to another lies the secret to understanding our wonderfully flexible number system.