Collections and What Is In Them
Last timeEvery, and At Least One
A collection described by a rule rather than a list, and the four ways of combining two of them. The notation is light and it is what every later claim about all cases is quantified over.
Every claim so far has been about something. Every order, at least one request,
all the whole numbers. The something is a collection, and this lesson gives it
enough notation to be worked with.
It is a short lesson. Nothing here is difficult and all of it is used
constantly.
Giving a collection by a rule
Small collections can be listed: the days of the weekend, the three retry
limits we support. Everything else needs a rule.
- the collection being defined, here the large orders
- a stand-in for one item, which the condition is applied to
- is an item of, so x \in B says x is one of the orders in the batch
- the collection the items are drawn from, here the batch
- read as such that, separating where the items come from and what they must satisfy
- the condition deciding membership, which must be definite for every x
Two relations get confused here, so it is worth separating them now. One order
is an item of the batch. The large orders form a collection sitting inside the
batch. The first relation holds between an item and a collection, the second
between two collections, and English says in for both.
The lesson stops here
1 more paragraph to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents