If the set of all strings of composite length is a regular language, you can use that to prove the set of all strings of prime length are also a regular language.

But it’s also easy to prove that the set of language of strings of prime length is not regular, and thus the language of strings of composite length also can’t be regular.

A more formal proof.

You got downvoted here but you’re absolutely right. It’s easy to prove that the set of strings with prime length is not a regular language using the pumping lemma for regular languages. And in typical StackExchange fashion, someone’s already done it.

Here’s their proof.

Claim 1: The language consisting of the character 1 repeated a prime number of times is not regular.

A further argument to justify your claim—

Claim 2: If the language described in Claim 1 is not regular, then the language consisting of the character 1 repeated a composite number of times is not regular.

Proof: Suppose the language described in Claim 2 is regular if the language described in Claim 1 is not. Then there must exist a finite-state automaton A that recognises it. If we create a new finite-state automaton B which (1) checks whether the string has length 1 and rejects it, and (2) then passes the string to automaton A and rejects when automaton A accepts and accepts when automaton A rejects, then we can see that automaton B accepts the set of all strings of non-composite length that are not of length 1, i.e. the set of all strings of prime length. But since the language consisting of all strings of prime length is non-regular, there cannot exist such an automaton. Therefore, the assumption that the language described in Claim 2 being regular is false.

Average Matt Parker code

“at least 2 characters repeated [at least] twice” implies the string’s length is divisible by a number greater than 1.

Yeah but it’s just so tempting… It validates so many inputs so easily…

They said—

A line with exactly 0 or 1 characters, or a line with a sequence of 1 or 3 or more characters, repeated at least twice

Note—

…or a line with a sequence of 1 or 3 or more characters, repeated at least twice

It should be—

…or a line with a sequence of 2 or more characters, repeated at least twice

The regex in the post will match “abab”. Their original description (line 2 of this comment) will not match “abab”.

Economic murder-suicide pact

It’s a line with a sequence of two or more characters repeated at least twice.

Yeah, and what the fuck else might I be referring to, hmmmm?

What is Hygge?

Yes, they’re similar, but from what I’ve heard, most UK building societies are basically the same as or worse than banks in terms of fees, rates, and service quality. In the US, most credit unions will absolutely spank the big banks on at least two of those, if not all three.

Oops, I didn’t see that. My bad. Guess I made a fool of myself here.

Well, you see, that depends on whether you have a team of highly-paid defence lawyers that can get you off if the prosecution makes even the slightest mistake in their case.

Okay, have a good day. I voted for Harris.

You’re free to disagree with the way the American legal system is structured. I’m not here to argue with you, and in many ways, I actually agree with you wholeheartedly that Garland would make a terrible judge in my notion of an ideal legal system.

The role of a judge in an inquisitorial system is to answer the questions “Did they do it? Do they deserve to be punished?”

In the traditional English system, this is the role of the jury. The judge is just there to ensure everyone is playing by the rules of the court. And in that role, Garland is pretty suitable. And yes, a sense of fairness and impartiality is not strictly required. Just a sense of logic, which Garland definitely has. You can correctly describe that as a fault of the legal system.

I apologise if you find this insulting.

Think of the judge in My Cousin Vinny. Do you think that he walked into that courtroom every day thinking “these idiots definitely did it”? It’s very likely he did. But he also recognised it wasn’t his job to broadcast that to the court. He had to put on a mask of neutrality because he recognised that it is the jury’s role to determine guilt, not his. He doesn’t need to be truly impartial to the defence’s case; he just needs to make the correct evidentiary and legal rulings. Which he mostly did.

Contrast that to the role of the prosecutor, which is what the attorney-general is. It’s the prosecutor’s job to come into court thinking “these guys are guilty” and convince the jury of the same.

Your position and view towards the law is admirable and very worthy of respect, but you are holding him to a standard that is not applicable within a legal system based on the traditions English common law, like the American one. You’re describing the role of a judge in an inquisitorial system, not an adversarial system.

The role of a judge in an inquisitorial system is to answer the questions “Did they do it? Do they deserve to be punished?”

In the traditional English system, the is the role of the jury. The judge is just there to ensure everyone is playing by the rules of the court.

Of course, it is impossible for anyone to be truly divested from personal opinion and bias. We are all human, after all. The guiding design principle of an inquisitorial system is that judges are expected to be as neutral as possible, and then the legal system presumed they succeeded. An adversarial system, on the other hand, is aware of the inherent biases of mankind and attempts to design around them.

Which approach is more valid is a long-running topic of debate in philosophy.

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You do not need to “pursue justice” as a judge. You just need to allow others to pursue justice through you and possess an ability to apply the law. There are no political repercussions for judges that can harm their career. He acts the way he does because he doesn’t want political backlash about it. If he’s a judge, he has the ability to not care about others’ opinions of his rulings.

The position of attorney-general requires a different skillset and mindset. An effective attorney-general is willing to take risks to pursue justice. Judges play a more passive role. That’s why he’s not a good attorney-general, but I still maintain he’d be a very good judge.

Lemmy has the tendency to think that because a person is bad in one aspect, they must be bad in every related aspect as well. Of course, nobody will admit they think like that, but I pray you don’t.

I will start. I’m in the United States.

Credit unions! Nearly half of all Americans are credit union members. They don’t seem to be popular in Europe and Asia. A credit union is a not-for-profit co-operative financial institution that essentially provides all the same services as a bank, except it’s run as a democratic institution with directors elected by the customers instead of as a profit maximisation machine for shareholders.

Rule 0 of warfare: don’t start a war if you don’t want the consequences of war.