The Sum Sign Is a Loop
Last timeSomething In, Something Out
The big sigma abbreviates an addition. Expanding one by hand, and compressing a long addition back into one, is the whole of the skill.
The big sigma is the mark that stops the most readers, and it is the easiest
one in the whole of notation, because it is not a mathematical idea at all. It
is an abbreviation for writing out an addition.
That is the entire content of the symbol. Everything else in this lesson is
about reading the three decorations around it correctly.
Expanding one
The sign carries a counter, a start, a stop, and a term.
Underneath the sign is the counter and the value it starts at. Above the sign
is the value it stops at, inclusive. To the right of the sign is one term,
written once, with the counter standing in for whichever term it happens to be.
To expand, write the term out once for each value the counter takes, and put
plus signs between them. That is a mechanical operation with no judgement in
it, and doing it on paper two or three times is enough to stop finding the
symbol difficult.
The lesson stops here
8 more paragraphs 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