ellipsis

in typography, an ellipsis is the name for three adjacent full stops, usually signifying an omission of something predictable by context.

in desmos, the ellipsis is an operator used for arithmetic progressions.

usage

for creating lists

to create a list of a subset of an arithmetic progression, type something like $\left[0,1…10\right]$. the first number is the starting value, in our case \(0\). the third number is the stop value, which will be the last value in that list. the second number is a little bit trickier: it’s the second item of our list. it is equal to start + step (step is by how much each item is incremented).

using our previous example, \(\left[0,1…10\right]\) will give us the list $\left[0,1,2,3,4,5,6,7,8,9,10\right]$. you can see how each item is one more than the previous one.

arithmetic progressions may also be negative. say you want a countdown from 100 to 0, but only with even numbers. then intuition suggests the step should be \(-2\) (negative since we’re going down), and the start and stop values are \(100\) and \(0\). using the already described syntax, that countdown will be generated by $\left[100,98…0\right]$. we got \(98\) as the second value because it’s start (\(100\)) plus step (\(-2\)). \(100+(-2)=98\).

you can omit the second value. in that case, the step will be automatically set to \(1\) or \(-1\) depending on the list.

for indexing lists

say you have a list \(L\) and you want to get all items including the third one and after the third one. no problem! you type $L\left[3…\right]$. to get items between the fifth one and the seventh one, type $L\left[5…7\right]$.

if you want to get the items in reverse order, you’ll need to set the start index bigger than the stop index. to get the entire list reversed, you can do this: $L\left[\operatorname{count}\left(L\right)…1\right]$