How so? It's bounded by the large initial triangle. The line containing any two of the vertices doesn't intersect any other point.

Obvious caveat: The points can't all lie in the same line (the collinear condition).

Not-so-obvious caveat: There can't be an infinite number of points.

Exactly, so when she reviewed the notebook, she caught the error.

Even if she made a slip in the notebook, merely reviewing it helps jog the memory to revisit and replay what she did in the lab. It's the power of touchstones.

> What if you have to do several steps rather quickly? Say adding a particular chemical, then waiting for ten seconds and adding, another chemical? Do you have time to write it down?

The notebook doesn't always have to operate as a log. It can also operate as a plan of action.

The present fix is to sanitize user input. Does it cover all cases?

“My point today is that, if we wish to count lines of code, we should not regard them as ‘lines produced’ but as ‘lines spent’: the current conventional wisdom is so foolish as to book that count on the wrong side of the ledger.”

https://news.ycombinator.com/item?id=46085897

That's an assumption increasingly false, unfortunately. The spirit of collegiality has been beaten back.

Far better to hone logical skills that sift between fact and error than to rely on social reputation. Ironically we're discussing a text designed to do exactly that.

The savvy LLM user already knows to be on the lookout for falsehood, if not bad pedagogy. That's a benefit, not a drawback of LLMs.

Following Dijkstra’s EWD1094, here’s a way to solve the hairs-on-heads problem eschewing the language of pigeonholes and employing the fact that the mean is at most the maximum of a non-empty bag of numbers.

We are given that Boston has 500,000 non-bald people. The human head has at most 200,000 hairs. Show that there must be at least 3 people in Boston who have the same number of hairs on their head.

Each non-bald Bostonian must have a hair count between 1 and 200,000. The average number of such people per hair count is 500,000 / 200,000 = 2.5. The maximum is at least that; moreover, it must be a round number. So the maximum >= 3. QED.

> By that logic the US shouldn’t get involved in any other foreign entanglement or global police action because of unintended consequences.

Strawman. No-one is claiming that.

Where is the right you're seeing?

For fun, try strengthening the result to a square.

Contrast Lord Kelvin: “When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarely, in your thoughts advanced to the stage of science.”

And also this doozy writ large in our lives: “If you can’t measure it, you can’t manage it.”

Not everything that counts can be counted.