Stash
rustc -C prefer-dynamic.meter-text { white-space: pre-wrap; }launchctl stop com.apple.pboard
launchctl start com.apple.pboard# requires ImageMagick
function img() {
identify -format '<img src="%f" width="%w" height="%h" />' $1
}References
Rudin Crib Notes
Brevity has been chosen over accuracy because the whole point is that you should know this stuff already.
Chapter 2: Basic Topology (+ some Ch. 3)
An isolated point of E is in E but not a limit point of it. E is perfect if it is exactly equal to its set of limit points. Equivalently, it is closed and has no isolated points. Ex. 2.44: The Cantor set is perfect.
A compact set is a set for which every open cover has a finite subcover.
Compactness or compact sets have these properties (with made-up names):
Problem Reference
(ported from wiki)
Certain notable problems that I don’t want to look through a zillion pages to find.
Iran TST 1996, notoriously reposted at least 35 times on AoPS (okay, many of these are actually modifications):
If \(x, y, z > 0\) then
\[(xy+yz+zx)\left(\frac{1}{(x+y)^2} + \frac{1}{(y+z)^2} + \frac{1}{(z+x)^2}\right) \geq \frac{9}{4}\]
ISL 1988 #4: if \(1, 2, \ldots, n^2\) are placed in a \(n \times n\) chessboard, some two adjacent numbers differ by at least \(n\)