Prelude on functions and graphs

This short video is a prelude to the next near-numbers video proper; it's a quick review of functions, focusing on how to properly use the graphs of real-valued functions. After this video, you in principle know how to apply a function to a near-number as well:

• put your input near-number on the domain axis, 
• push those points up to the graph, 
• push them over to the codomain axis, 
• then let your near-number squeeze to see the result!. 

We'll go through this for a bunch of important examples in the next video (it might take a while to produce, as the animations for functions are a bit involved!), but for now, here's the prelude:

Lesson 2: The Arrow Relation

The learning goals for this video are as follows:

1. to understand what it means for one near-number to "fit into" or "not fit into" another one, both intuitively and in terms of slices, and to be able to determine and explain whether one near-number fits into another or not;
2. to understand what it means for a near-number to converge or diverge, along with the notion of limit, and to be able to determine and explain which of these a given near-number does;
3. to understand what it means for an arrow statement to be indeterminate for a near-number, to be able to explain indeterminacy, and to give examples of it.