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.
That’s because you use English, a language where ordinals traditionally begin at one.
My argument is purely pedantic. Pedantry is the lifeblood of programmer “humour”.
I’m not arguing that we should adopt zero-based numberingin real-life human applications. I am arguing that in zero-based numbering, the label “zeroth” refers to the same ordinal as “first” in one-based numbering. I am poking fun at the conversion between human one-based numbering and computers’ zero-based numbering. That is why I am saying it should be called zeroth(); because human language should adapt to match the zero-based numbering their tools use. Whether I actually mean what I say—well, I leave that up to you.
It does not matter why indexes start from zero in computing. The memory offset argument is only salient if you are using it as an argument for why computers should use zero-based numbering. It is not an argument against the properties of zero-based numbering itself.
Zero-based indexing redefines the meaning of the labels “first”, “second”, “third”, and so on. It adds a new label, “zeroth”, which has the same ordinal value as “first” in one-based indexing. The word “first” does not mean “the element with the lowest index” in zero-based indexing.
If you are using a zero-based numbering system, you would absolutely say that array[2] is the final element in the array, that element having the ordinal label “second”, and yet the length of the array is 3 (cardinal). There is no fundamental connection between the ordinal labels “zeroth”, “first”, “second”, and “third” and the cardinal numbers 0, 1, 2, and 3. The similarities are purely an artefact of human language, which is arbitrary anyway. You can make an equally mathematically valid ordinal numbering system that assigns “third” to the element with the smallest index, “fourth” to the next-smallest, and so on. That ordinal numbering system is mathematically coherent and valid, but you’re just causing trouble for yourself when it comes time to convert those ordinals (such as array indexes) into cardinals (such as memory locations or lengths of fencing to buy).
You can make an argument for why one-based numbering is more convenient and easier to use, but you cannot use the notion that zero-based numbering doesn’t make sense given the assumed context of one-based numbering as an argument for why zero-based numbering is invalid.
I encourage you read up what is meant by “zero based numbering” because you and everyone else who has replied to me has tried to use “but that’s not how it works in one-based numbering” as an explanation for why I’m wrong. This is as nonsensical of an argument as trying to say i (the imaginary unit) is not a number because it’s not on the number line. It’s only not a number in the domain of the real numbers. Similarly, zero-based numbering is only nonsensical in the context of one-based indexing.
It does not matter why indexes start from zero. The memory offset argument is only salient if you are using it as an argument for why computers should use zero-based numbering.
Okay, I will admit, you got me there. I did confuse indexing with numbering. From now on I will use the term “numbering” instead.
It is entirely how ordinal numbers work in zero-based numbering. There is no “right way” for ordinal numbers to work. You can create a valid ordinal numbering system starting from any integer, or just some other ordered list. You cannot assume one-based numbering is “correct” and use it as an argument against numbering beginning from any other number.
I encourage you read up what is meant by “zero based numbering” because you and everyone else who has replied to me has tried to use “but that’s not how it works in one-based numbering” as an explanation for why I’m wrong. This is as nonsensical of an argument as trying to say i (the imaginary unit) is not a number because it’s not on the number line. It’s only not a number in the domain of the real numbers. Similarly, zero-based numbering is only nonsensical in the context of one-based indexing.
Zero-based numbering would number “foo” as the zeroth element, “bar” as the first element, and “baz” as the second element. “zeroth”, “first”, and “second” are labels representing ordinals. Your list has a length of 3 (which is a cardinal quantity unrelated to ordinals).
Although, I would like to point out, it is perfectly valid to construct an ordinal labelling system that assigns “fifth” to the element with the lowest index, “sixth” to the next, and so on. That system is mathematically coherent but it is just troublesome to when it comes time to convert ordinal numbers (such as the index of the last fence-post) to cardinal numbers (such as the length of fence to buy).
But this is now getting into the weeds of pure mathematics and most people here are engineers.
That’s because the word “first” in first() uses one-based indexing. In true programmer fashion it would have been called zeroth() but that is wholly unintuitive to most humans.
I maintain that the element with the lowest index is called the “zeroth” element in zero-based indexing and “first” in one-based indexing. The element with index N is the Nth element.
Bullshit.
Every programmer knows that 'A' in ['A', 'B', 'C', 'D'] would be the 0th item; the first item is 'B'
Rulers measure cardinal quantities and not ordinal ones. There is no cardinal numbering scheme that starts at 1, all of them “start” at 0. For ordinal numbering schemes, the symbols are arbitrary anyway and you can start with whatever you want. It’s equally valid to start with 1, 0, -1, A, or “aardvark”. The only benefit to picking 1 as the start is to make it easier to count with your fingers while picking 0 lets you easily convert an ordinal quantity to a cardinal one.
I have a script running that uses the Namecheap API to automatically get wildcard certs from Let’s Encrypt. I didn’t pay a dime for this. Did something change?
Nothing wrong with Boost Mobile, or any other discount telecom provider either. It’s not like the phone signals taste different lmao
It’s just a hallmark of “I bought the cheapest domain name TLD available”.
That’s not necessarily bad if all you need is something to get the job done, but there is a stereotype associated with it.
I think it is generally okay to bundle the root domain certificate and the wildcard for its subdomains into a single renewal.
So for example:
example.com
*.example.com
The data is all stored server-side. The worst that could happen is the sync connection stops working and you need to redownload the files. Nothing gets deleted by these commands. They will still be on your disk and accessible by you.
If this breaks Nextcloud, it indicates something’s wrong with your installation.
Contabo is cheap but has some weird quirks. I pay about five euros a month. My server got mysteriously rolled by two days and they denied anything happened to it. I restored from backups but it was odd.