FILE SELECTED // FILE 00
Necessary and Sufficient Conditions
“What is required may not be enough; what is enough may not be required.”
01 / SUMMARY
In short
A necessary condition must hold for something to occur. A sufficient condition guarantees the result. A relation may play only one role or both.
03 / SCENE
In the wild
Oxygen is necessary for ordinary combustion, but not sufficient: fuel and an ignition source are also needed.
04 / LIMIT
The limit
Calling X a requirement does not mean X produces the result on its own.
FINAL NOTE
What remains
Translate each claim: is the result impossible without X, or guaranteed with X?