Introduction to set theory

Welcome to my introduction to set theory, in which I’ll cover just the very basics, and which should only take about 5 minutes for anyone of average intelligence. If you’re below average intelligence you can come back as many times as you wish and work through it at your own pace. To make it easy to understand I’ve chosen a subject that’s topical to introduce the basic concepts. Take a look at the first figure, below. This shows two sets, labelled US and THEM.

SetTheory1 In this example US is the group of people in employment, strivers, people who graft to support themselves and their loved ones. Good people, tax payers, people like you and me.

The second group, THEM, is the group of people on Jobseekers Allowance (JSA). These people do not work. They’re the scroungers, living on money that comes from US, the workers.

As you can see the two sets are distinct in that people are either employed or claiming JSA, but not both. This makes it easy to see that people are either strivers (US) or scroungers (THEM).

I have a confession to make at this point. Up until last June I was one of US, the employed, the strivers, but then I became one of THEM for almost six months before becoming one of US again. Other than that, I’ve spent almost the whole of my life since leaving school at 16 as one of US, so for the moment let’s consider it a blip (we’ll come back to it later). If I’m honest, I never really considered myself to be one of THEM because I was unemployed through no fault of my own, being made redundant, and even though I was claiming JSA I promise I spent every day looking for work.

Now, that gives me the opportunity to introduce the concept of a subset because THEM, the people claiming JSA, includes all of the people claiming JSA (obviously) but only some of them are really scroungers in the dictionary sense of the word. The rest are people who would belong to US if they could, generally well-meaning people like us, and not scroungers. My second diagram, then, represents this grouping.

It shows US, the employed people or strivers, and SetTheory2THEM, the people claiming JSA, but it also shows that within THEM is a subset, people who are genuine dictionary-sense scroungers, as opposed to those claiming JSA but with an aspiration to work. As someone who spent time last year claiming JSA I feel more comfortable with this. It reflects that for a while I was one of THEM but doesn’t label me a scrounger.

Now this may be more complex than you’re used to when discussing, thinking about or reading about this subject, and it may be more complex than you’re used to seeing it presented by, say, politicians and the media, but for the purpose of our simple introduction to set theory it works quite nicely. If you’re finding it difficult to grasp, don’t worry, just read through the above and take a look at the second diagram, and work on it until you’re comfortable with the idea of subsets, because you’ll need a firm grasp on the concept if you’re to understand the final part of my introduction.

Yes, there is a final part, one more step, because I’m afraid there is still something about the second diagram that doesn’t quite ring true. Take a look at my third and final diagram.

This takes the concept of subsets oneSetTheory3 step further. It shows the scroungers as a subset of those on JSA as before, but also shows all of those on JSA as a subset of US. In this diagram, there is no THEM. Take your time. Think about it.

In this diagram US contains all employed people and JSA claimants. Within US is the subset of those claiming JSA. Those outside of this subset are the workers, strivers, those we represented in a distinct set in the first two diagrams. Both groups are now part of US.

Within the JSA set is a smaller subset, the scroungers. I know it can get uncomfortable for some people here, but the scroungers are still US. They’re the US that are not working and, although claiming JSA, don’t have an aspiration to become one of the employed. The scroungers are not always easy to recognise, they may look just like other JSA claimants or even like the employed, but though they’re sometimes hard to recognise we know they exist and can consider them as a subset of US.

This, I think, is a better model than the first two diagrams. There is no longer an US and THEM, only an US. Some of US are employed and some of US are not. Importantly, membership of these sets is not fixed for all time. Some people move from the employed set into the unemployed set. Some move from the unemployed set to the employed set. That’s what happened to me, I was one of US who is employed, then I became one of US who is unemployed, then I became one of US who is employed again, and though I know that many people speak of US and THEM, I always felt that I was still one of US. Today you, your wife, husband, daughter, or someone else you love, may be one of the employed, but tomorrow you or they may be claiming JSA, but you’ll still be one of US, okay? It’s all in the diagram. It’s unlikely that you’ll become one of US who is a scrounger unless you have the mind-set and aptitude for it, and not everyone does, but they’re US too even if we don’t like it, the US who don’t work and don’t want to work.

Once we stop thinking about US and THEM it all becomes easier to understand.

That completes my introduction to set theory. I hope you’ve found it interesting and potentially useful.