codeismightier

Intriguing claim! At first I was skeptical, thinking that there would be an issue with leading zeros being discarded. However, with some piloting, I was able to use Claude and ChatGPT to construct a proof of your claim.

Sketch of the argument:

First, an arithmetic coder maps strings to non-overlapping subintervals of [0, 1) that respect lexicographic order.

Second, the process of emitting the final encoding preserves this. If enc(s) ∈ I(s), enc(t) ∈ I(t), and I(s) <= I(t), then enc(s) <= enc(t).

Finally, binary fractions compared left-to-right bitwise yield the same order as their numerical values — this is just memcmp.

Thus, we have a proof of your claim that arithmetic coding preserves lexicographic order! Nice result!

My mistake was in thinking that leading zeros are discarded -- it is tailing zeros that are discarded!

Both S-Corp and LLC are pass-through entities; there is no difference in terms of tax treatment.

Money is just an abstraction for actual goods and services produced by the economy. If your wages go up, presumably so does the wages of those whose services you consume.

If less people worked, the economy would produce less and we would be worse off.

Can you explain a bit more about how these people can raise their standard of living by moving?

Money is just an abstraction for real goods and services produced by the economy. Presumably we need people to live in Philly since that's where our industry is. If people moved away to some remote place, wouldn't our economy take a hit? Not to mention the transportation costs of servicing a more remote, less dense area.

Housing is, to a certain extent, a positional good. People want to live in safe, friendly neighborhoods, surrounded by well educated, middle to upper class people. Even if everyone got more money, it's not easy for more people to live in desirable neighborhoods (at least without changing the character of those neighborhoods).

If the inventor is a corporation, this would be gamed by simply transferring ownership of the corporation. If the inventor is a human, the person would have to organize as a sole proprietorship and forgo limited liability. Designing rules is hard!

You are right that it was a bad argument :). As such I've deleted the comment.