MathML

Author: MatthijsBlom

source_md/higher-order-functions.md

@@ -796,14 +796,16 @@ ghci> scanl (flip (:)) [] [3,2,1]
 When using a `scanl`, the final result will be in the last element of the resulting list while a `scanr` will place the result in the head.
 
 Scans are used to monitor the progression of a function that can be implemented as a fold.
-Let's answer us this question: **How many elements does it take for the sum of the square roots of all natural numbers to exceed 1000?**
+Let's answer us this question: **How many elements does it take for the sum of the square roots of all natural numbers to exceed $1000$?**
 To get the square roots of all natural numbers, we just do `map sqrt [1..]`.
 Now, to get the sum, we could do a fold, but because we're interested in how the sum progresses, we're going to do a scan.
-Once we've done the scan, we just see how many sums are under 1000.
-The first sum in the scanlist will be 1, normally.
-The second will be 1 plus the square root of 2.
-The third will be that plus the square root of 3.
-If there are X sums under 1000, then it takes X+1 elements for the sum to exceed 1000.
+Once we've done the scan, we just see how many sums are under $1000$.
+The first sum in the scanlist will be $1$, normally.
+The second will be $1 + \sqrt 2$.
+The third will be $1 + \sqrt 2 + \sqrt 3$.
+If there are $n$ sums under 1000, then it takes $n + 1$ elements for the sum to exceed $1000$.
+
+
 
 ```{.haskell:hs}
 sqrtSums :: Int
@@ -820,7 +822,7 @@ ghci> sum (map sqrt [1..130])
 ```
 
 We use `takeWhile` here instead of `filter` because `filter` doesn't work on infinite lists.
-Even though we know the list is ascending, `filter` doesn't, so we use `takeWhile` to cut the scanlist off at the first occurrence of a sum greater than 1000.
+Even though we know the list is ascending, `filter` doesn't, so we use `takeWhile` to cut the scanlist off at the first occurrence of a sum greater than $1000$.
 
 ## Function application with $ {#function-application}