The Rodeo

I have been asked by Kim and Jason to take part in their Adultitis Escape Plan, a 40-day plan to become more childlike (not childish)
and to reduce stress and prevent dullness, depression and [insert
another word beginning with ‘d’ here]. Of course I’m gonna do it.

Dreary-ness, that begins with ‘D’.

As not everyone who reads my stuff has done university level maths (where I learned this topic), I am going to give a (very) brief overview of set theory.

Ok, so to start, a definition: A set is a collection of unique objects.

Yep, that’s it. A collection of unique objects. That means that in the set of numbers from 1 to 10 I would have: {1, 3, 2, 5, 4, 9, 7, 8, 10, 6}. If you want to have multiple copies of a number in there, it would stop being a set and start being a list. So the fibonacci numbers (0, 1, 1, 2, 3, 5, 8, 13) are a list, not a set.

You might have also noticed in that set there is no given order - that’s because sets don’t have  an order. They are just a collection of values.

That’s the definition, but not very useful on it’s own. However, using sets in combination can be quite useful.

An example is probably in order. Say I have two sets: the set of number between 1 and 10 (as given above) and a set of numbers that are multiples of 3  {3, 6, 9, 12, 15, 18}. Using these two sets I can find the set of numbers that are multiples of three and under ten.

To find this set we perform what is known as an intersection - that is, where the two sets intersect each other, or where they overlap when you put them on top of each other.

So the resulting set is {3, 6, 9}.

The other major thing you can do with sets is a union. A union is quite simply putting the combination of two sets together. So, lets take our set that we created last time: {3, 6, 9} and combine it with the multiples of two that are less than ten: {2, 4, 6, 8}.

The resulting set this time is {2, 3, 4, 6, 8, 9} (notice how the 6 only ends up in the set once).
Not hugely interesting, but you can use these two procedures to find out lots of useful things with sets.

Now a real world example.

I usually have peanut butter and vegemite on my sandwiches. So that means I would have the set of sandwich ingredients like so: {PB, V}. I also like to have peanut butter and honey on sandwiches: {PB, H}. So, considering each sandwich a set of toppings, we can perform an intersection and find out that I like having peanut butter on my sandwiches - the intersection of the two sets is {PB}.

Now, we can also perform a union on the two sets here and find another combination that I might also like.

The union of the two sets of sandwich toppings I like provides this {PB, V, H}.

So, it seems like a good sandwich for me to try would be peanut butter, vegemite and honey.

… insert 5 minutes here…

Not too bad. It’s like eating dinner and dessert at the same time. The vegemite is pretty salty, and the honey is quite sweet, and the peanut butter… it’s peanut butter. Probably not what I would eat every day, but it wasn’t the horror I imagined it would be.

There you go then, a lesson on set theory, and a tasty snack.

RodeoClown: really does eat this stuff.

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