“The legislation on sex outside marriage and cohabitation is complaint-based, with only a husband or wife of a married person or the parents or children of an unmarried person able to report a matter to police. That means de facto foreign couples effectively can’t be denounced to authorities.”
If the law were to limit complainants to permanent residents and citizens, not overseas family members, it would not be a problem for tourists.
Define lim without infinite sets. Define how you quantify over all values of n without infinite sets. The parameterization you describe would be a function mapping an infinite set of sets of natural numbers to their maximum elements, that function itself being (or containing) an infinite set of ordered pairs.
You might be able to pull it off without creating something equivalent to the axiom of infinity — I wouldn’t know if it’s possible. But the naïve implementation of your ideas involves the construction of infinite sets.
I think you can do this rigorously outside the theory, talking about it, but not inside.
One construction of the natural numbers that I've seen is
1. There exists an element 0 that is a natural number
2. For every natural number there is a "sucessor" that is also a natural number. (i.e. if n is a natural number then n+1 is a natural number)
This construction means there can't be an upper bound N because then step 2 couldn't be applied to N.
Maybe there are other constructions that could workaround this? I'm guessing not because you'd still struggle to define the usual rules of addition for all numbers in a bounded set
> This construction means there can't be an upper bound N because then step 2 couldn't be applied to N.
Bendegem discusses this problem at length in his paper [1]. As programming-heavy site, I assume we're all aware that computers have finite resources. The universe too has finite resources so no matter how big a computer you build, it too will be finite. Therefore the infinity that is so pervasive in math is unphysical in a very real sense. So what would math look like and how would theorems change if this finiteness were formalized? That's what various flavours of finitism aim to achieve.
So to get back to your question as to the nature of the naturals, it seems evident that yes, at some point, you literally can fail construct the natural number N+1 if you are given N, because you will run out of particles in the universe. What implications this will have for various theorems will be interesting for sure, but it isn't clear yet because finitism isn't given much funding.
Edit: however, it's clear that some very unintuitive results follow from the infinities embedded in mathematics, and that a finitist approach resolves some of them. For instance, the argument that "0.9999... = 1" is true in classical mathematics while this equality is arguably not true under strict finitism because "0.999..." does not exist, because infinite objects do not exist, and so it will never equal 1.
Calling “0.999… = 1” very unintuitive is a very strange thing to say, because that makes perfect sense to most children. I’d like to see a result that truly is unintuitive, like what we get with the axiom of choice.
I remember being a kid and having this discussion in elementary school. Kids have enough intuition to know that operations with fractions should get the same result as with decimal numbers. Or that 1-0.999… = 0.000…. Or that different lengths have a length in between them. All are legitimate and compelling arguments.
I think lots of students get lost with different orders of infinity (countable, uncountable, etc.), so I think there is definitely a point beyond which you can't push the intuition behind infinite objects.
She didn't get to the Supreme Court because she was forced to serve a client whose conduct she disapproved. In fact, this case doesn't involve a specific client at all. This case is about the would-be client that hasn't even walked in the door.
And the court isn't considering whether LGBTQIA+ people fall into a protected class category, that's not this case. Metaphorically, this case is whether or not she can put up a sign on her business's front door that says "No ___ allowed." And according to the article, this conservative SCOTUS appears to be sympathetic to the "No ___ allowed" sign.
It appears SCOTUS is trying to draw line between public accommodation businesses and businesses that create speech, a distinction I believe Justice Sotomayor and KBJ countered aptly.
I could imagine an ISP denying the use of its networks to LGBTQIA+ people because they have sincerely held religious objections to transmit those customers' data across their network.
Marrying someone of the same sex is a behavior, and the designer is refusing to design websites relating to that behavior. The designer didn't refuse to design a website for say, dog walking just because the client is gay.
The debate is over Colorado law that, according to the article, "bars businesses open to the public from denying goods or services to people because of race, gender, sexual orientation, religion and certain other characteristics."
I understand wanting to make the distinction between objectionable behavior and the intrinsic characteristics of clients. But that's not a distinction the Colorado law considers. And if stuck down, SCOTUS could establish that there would be nothing baring a business to refuse service to LGBTQIA+ dog walkers.
> Smith explains that she decides whether to take on a commission based on the message that the work will convey, rather than the person requesting it. This means, she says, that she would “happily” design graphics for an LGBTQ customer who runs an animal shelter. But she will not take on commissions that would be inconsistent with her Christian beliefs – including, she says, by promoting same-sex marriage – because a custom wedding website would “express approval of the couple’s marriage.”
> Smith warns that allowing the 10th Circuit’s ruling to stand would mean that artists will be required to engage in speech that violates their conscience. Calligraphers who support abortion rights can be compelled to create flyers for anti-abortion activists, she says, and musicians who are atheists can be required to perform at religious ceremonies.
Well, maybe. I can think of a couple of families in my neighborhood with offspring who could legitimately claim to be of African descent, but who could if they cared to pass as white or Asian (i.e. like Dad rather than Mom).
How does that help anything? That's not objective at all. There are white Africans (Elon Musk) and Europeans who can pass for northern Africans. You can also find siblings of which one could pass as black and the other as white.
The idea you can easily divide people in different race groups is literally the definition of racism. It doesn't work and we shouldn't be doing it.
You can also find siblings of which one could pass as black and the other as white. Sometimes even parents and children. Would they then be of a different race?
What are the different human races you can identify from appearance if I may ask?
My point is that race is a very loose definition which quickly falls apart in practice, and thus it's just plain stupid to use it to decide whether people should be admitted to college or not.
“The legislation on sex outside marriage and cohabitation is complaint-based, with only a husband or wife of a married person or the parents or children of an unmarried person able to report a matter to police. That means de facto foreign couples effectively can’t be denounced to authorities.”
If the law were to limit complainants to permanent residents and citizens, not overseas family members, it would not be a problem for tourists.