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.
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”.
It’s a line with a sequence of two or more characters repeated at least twice.
It’s not really like they were evil about it though. Google attracted customers through its huge (at the time) 1 GB email storage space, which at the time, was unbelievably generous and also impressive in that it was offered for free. Outlook (Hotmail at the time) also drew in customers by offering the service for free, anywhere in the world, without needing to sign up for Internet service. Remember, at the time, e-mail was a service that was bundled with your Internet service provider.
Into the mid-2000s and 2010s, the way that Gmail and Outlook kept customers was through bundle deals for enterprise customers and improvements to their webmail offerings. Gmail had (and arguably, still has) one of the best webmail clients available anywhere. Outlook was not far behind, and it was also usually bundled with enterprise Microsoft Office subscriptions, so most companies just decided, “eh, why not”. The price (free) and simplicity is difficult to beat. It was at that point that Microsoft Outlook (the mail client, not the e-mail service) was the “gold standard” for desktop mail clients, at least according to middle-aged office workers who barely knew anything about e-mail to begin with. Today, the G-Suite, as it is called, is one of the most popular enterprise software suites, perhaps second only to Microsoft Office. Most people learned how to use e-mail and the Internet in the 2000s and 2010s through school or work.
You have to compare the offerings of Google and Microsoft with their competitors. AOL mail was popular but the Internet service provided by the same company was not. When people quit AOL Internet service, many switched e-mail providers as well, thinking that if they did not maintain their AOL subscription, they would lose access to their mailbox as well.
Google and Microsoft didn’t “kill” the decentralised e-mail of yesteryear. They beat it fair and square by offering a superior product. If you’re trying to pick an e-mail service today, Gmail and Outlook are still by far the best options in terms of ease of use, free storage, and the quality of their webmail clients. I would even go so far as to say that the Gmail web client was so good that it single-handedly killed the desktop mail client for casual users. I think that today, there are really only three legitimate players left if you’re a rational consumer who is self-interested in picking the best e-mail service for yourself: Proton Mail if you care a lot about privacy, and Gmail or Outlook if you don’t.
Baking soda is sodium bicarbonate. Dissolving it in water will increase its pH. I’m not sure if that works for killing bacteria.
Explosives don’t seem smart. Why didn’t they poison the chocolate instead? The enemy opens the chocolate, sees nothing wrong with it, shares it with their mates, and then now you’ve got five casualties who are none the wiser. Is that against the rules of war or something?
Pretty sure humans are not the most co-operative animals alive.
Bees and ants exist, you know
Uh oh. You should not have said that. Run for cover.
I know it’s a copypasta, but I correctly differentiated GNU and Linux in my comment.
Maybe so, but children don’t always adopt the ideology of their parents. They usually do, but not always.
That doesn’t make him a socialist. He doesn’t espouse any of the core socialist beliefs there. He’s just saying he’s a “woke communist” (as described by the right), which could mean anything from a centre-left liberal to a Marxist.
Doesn’t that make you a communist?
I would say GNU is one that’s openly socialist. If Linux’s (or rather, Linus Torvald’s) philosophy is socialist, they either do a very good job of hiding the fact or there is a lot I don’t know about them.
When you assume anyone complaining about .ml and Hexbear must be a liberal
I think every time a big leftist instance gets defederated, its users leave and move towards more mainstream instances. I remember lemmy.ml used to be somewhat neutral a year or so ago (I got banned there so here I am now on lemmy.world).
I want to be clear here that this is dangerous messaging. While any individual vote likely has little effect on the outcome of an election, it’s people’s collective vote that does ultimately decide the outcome. And when the electorate is disengaged, disinterested, and apathetic, that is the environment in which fascism and authoritarianism thrives. Voting is not and should not be the end of a citizen’s political participation, but it is still vitally important. Voting should only be the foundation of citizen political participation. It’s also important to campaign, to discuss important political issues with others, and to protest and take direct action against the injustice of the political class. But if you don’t vote and spread the idea that voting is meaningless, your efforts will change nothing.
This line in particular comes a lot of young people, and it is an absolutely understandable and reasonable conclusion for them to come from seeing as they are the most politically neglected group, and politicians almost never pay more than lip service to the concerns of the young. Youth turnout in elections is historically rubbish, so why would any rational politician pay heed to the demands of a voting bloc that won’t influence the outcome of an election? Politicians who pander to youth voters will lose to politicians who pander to old voters simply because youth voters will stay home while old voters will show up at the polls and vote their guy into office.
It costs almost nothing to vote and to encourage others to vote as well. So do it. It is irresponsible to spread the idea that voting is meaningless without also attaching the context that if you don’t vote, you have no power at all.