[escape_goat]

There is not, and there cannot be. However, even if he was figuring this all out from scratch, he could not have come up with the hand-written charts without realizing that.

I'm going to go out on a limb and guess that it is of some habitual relevance to a mathematician, since he mentions the identity function (not really relevant here either), but that the material he actually explains here doesn't do anything to justify its appearance.

However, I cannot present to you the crucial difference between the maximum of two numbers and the minimum of two numbers that explains what he was thinking. This must exist for my hypothesized explanation to make sense.

[thaumasiotes]

> I'm going to go out on a limb and guess that it is of some habitual relevance to a mathematician, since he mentions the identity function (not really relevant here either), but that the material he actually explains here doesn't do anything to justify its appearance.

It's worse than that; he mentions the identity function only to make a gross error about it. The identity function on (a, a) is (a, a), not a.

[coinomega]

I don't think you need to be so unforgiving?

If you want extra precision, a -> f(a, a) is Id.

Knowing that helped me understand one property of the chart, never said that was the most stunning of properties, and the best articulated one :-)

[jonsen]

The law x AND 1 = x is called the identity law.

The law x AND x = x is called the idempotence law.

Nothing to do with the identity function.

[thaumasiotes]

> If you want extra precision, a -> f(a, a) is Id.

What does this mean?

[coinomega]

The function which to any integer a associates f(a, a) with f defined as in the article is the identity function on the natural integer set.

[thaumasiotes]

Granted. g(a) = f(a,a) is indeed the identity function for all f such that f(a,a) = a. That seems pretty pointless as an observation. We have f, so we're observing that some other, unrelated function is the identity function?

[coinomega]

Assuming you actually care about the answer, this just help me drew the exploratory graph, and this property was useful to fill in cells for which operands were equal. Finding obvious properties is a great way to learn a pattern without even computing things. Unlike what you may think, I had no idea what I was about to find - I had never seen this chart drawn before, and so this post is structured around how I thought about the exploration, not around how it may be presented to an audience who already knows way more than I do on bitwise operations. Sounds fair?