Content and Encounter Are Two Different Counts
A reader meets part of a set, in some order. Divide possible encounters by possible contents and the factorial of what they met is left.
Definition
Many impressions
How Many Impressions a Content Allows
Arrangements, and why the author chooses none of them.
2 to 151 200
9 notes in this part
Why the Order Is Part of What Happened
Treating two readers who met the same statements in different sequences as having had the same experience throws away the larger of two numbers.
Reference
The Two Ceilings Sit on Different Pages
The shape with the most possible contents is not the one with the most possible encounters. The two maxima sit on different pages, for a structural reason.
Recount
Four Things That Are All Seven Hundred and Twenty
One number stands at four unrelated places in this record: three pages produce it as an arrangements figure, and it is also six factorial.
Caution
The Shapes With Only One Content
A reader who meets everything published leaves nothing to vary but the order. Twenty-five shapes are of that kind, and they are the clearest case here.
Reference
One Figure Is Not Enough to Name a Page
Three hundred and thirty-eight shapes take only thirty-five distinct arrangements figures. The contents figure identifies a page no better.
Recount
Two Figures Name the Page Exactly
Neither figure identifies a page alone. All forty-four pairs are distinct, and both original numbers come back out of a pair with two divisions.
Recount
What the Median of This Table Means
The median arrangements figure is two hundred and ten — a fact about how this table was built, not about sets of pages in the world.
Caution
What Publishing More Does to the Figures
Hold the published count at ten and vary only how much is met. Arrangements run from ten to one hundred and fifty-one thousand two hundred.
Analysis