Peerpedia demo — a template for your first note

--- Base version+++ Proposed version@@ -0,0 +1,79 @@+## Add the first few integers {#sec:sum}++Suppose we want the total $1+2+\cdots+n$, where $n$ is a positive integer. Pair the first term with the last. Each pair has the same sum. Writing the list twice, once in each direction, makes the pattern work for odd and even $n$ alike.++Inline mathematics goes between single dollar signs, as in `$n+1$`. A displayed equation goes between double dollar signs. Give it a label when you want to refer to it later.++````markdown+::: equation {#eq:sum}+$$+1+2+\cdots+n=\frac{n(n+1)}{2}.+$$+:::+````++::: equation {#eq:sum}+$$+1+2+\cdots+n=\frac{n(n+1)}{2}.+$$+:::++Equation references stay meaningful when earlier material is inserted. Write `@eq:sum` to produce @eq:sum instead of typing its number yourself.++### State the claim and explain it++Theorem and proof blocks separate a claim from its justification.++```markdown+::: theorem {#thm:sum}+For every positive integer $n$, the sum of the first $n$ positive+integers is $n(n+1)/2$.+:::++::: proof+Write the sum twice, once in each direction. Adding the two rows+term by term gives $n$ copies of $n+1$. Divide by two.+:::+```++::: theorem {#thm:sum}+For every positive integer $n$, the sum of the first $n$ positive integers is $n(n+1)/2$.+:::++::: proof+Let $S=1+2+\cdots+n$. Reverse the order of the terms in a second copy of $S$. Each column then adds to $n+1$.++$$+\begin{aligned}+S&=1+2+\cdots+n,\\+S&=n+(n-1)+\cdots+1,\\+2S&=n(n+1).+\end{aligned}+$$++Dividing by two gives @eq:sum.+:::++### Check a few cases++A table can carry a caption and a label too.++```markdown+::: table Small cases {#tab:sums}+| $n$ | Direct sum | $n(n+1)/2$ |+| --- | --- | --- |+| 1 | 1 | 1 |+| 3 | 6 | 6 |+| 5 | 15 | 15 |+:::+```++::: table Small cases {#tab:sums}+| $n$ | Direct sum | $n(n+1)/2$ |+| --- | --- | --- |+| 1 | 1 | 1 |+| 3 | 6 | 6 |+| 5 | 15 | 15 |+:::++The agreement in @tab:sums checks these examples. The proof of @thm:sum is what establishes the formula for every positive integer.