## Jeremy Côté

Bits, ink, particles, and words.

# One-to-One and Onto

When learning about functions, a few properties come up over and over. In particular, we often hear about functions being one-to-one (injective) or onto (surjective). These are important properties of functions that allow one to set up correspondences between sets (bijections), as well as study other features of various functions. I wanted to go through these two properties in a slightly different way than what most sources will do to explain them, so hopefully this will be a good analogy to keep on mind when discussing these two properties.

# Recipes

When you learn a new concept, chances are that there’s some sort of procedure to follow in order to come up with an answer to a problem. This helps students when they are first learning, because it lets them follow clearly laid out steps that will culminate in the correct answer. For example, if we were trying to add two fractions together, we know that a common denominator is needed. As a result, students might be told that they should multiply each fraction by the other’s denominator, which will guarantee that the denominators are the same. It might even be written in a nice three-step method like this: