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Partial orders can also have maximums
But maximums are only guaranteed to be represented by a unique element in in total orderings.
Edit: also, infinite sets might not necessarily contain an element of their maximum value.
There are demonstrably not infinite humans alive at the same time though.
Okay, so Earth exists. This means for a set volume of space (say about the size of the solar system) there is some positive probability that it contains a planet that is indistinguishable from earth. Let's assume the universe is infinite. If we can search an arbitrary volume instantly, our probability for finding a duplicate of earth approaches 1 as our volume increases. This means the probability we will never find a duplicate of earth is exactly 0, which means that we will find a duplicate upon searching a finite volume. Since in our hypothetical the search is instant, we can perform this search again, locating a second duplicate of earth. Following this process, we can locate an arbitrary number of perfect earth duplicates in a finite ammount of time. This means that if Earth arose from natural processes in an infinite universe, there are infinitely many exact duplicates of earth with life that includes specimens genetically identical to humans.
This implies that there is no one gayest person in the universe.
Eh.
You're starting from the assumption that the universe is infinite, and conclude that there is no maximum because the universe is infinite.
Sorry for being this blunt, but that's intellectually boring.
Most of the entertainment comes from the non-obvious corollaries of the intermediate results. For example, every person has infinitely many perfect yet distinct copies that are identical right down to personal histories.
There's more, if you care to take the time to think about them. I was just using the conversation as an excuse to expose more people to the implication.
There are infinities without repetition. Usually the proofs for the stuff you describe assumes finite possibilities.
Please elaborate.
There are an infinite number of numbers between 0 and 1, and yet there is no repetition. Pi and other irrational numbers are infinite yet non-repeating. I wish I knew the name for this kind of thing because I'm sure it's been discussed in philosophy (a kind of opposite, eternal recurrence, has been discussed a lot).
I don't think anyone knows enough about the universe to say whether or not there is infinite variety in macroscopic stuff, so I don't think anything can be ruled out.
I don't think anyone knows enough about the universe to say whether or not there is infinite variety in macroscopic stuff
There are finitely many particles in the observable universe (that is to say, an infinite number will not fit), and a finite granularity to discern the position of those particles. That means there are finitely many configurations of particles within the volume of the observable universe.
Therefore, there are finitely many discernable things, so in a meaningful sense we can say with confidence that there's a finite variety of macroscopic things.
Whether or not an infinite number of particles will fit or not is not important, no ? I'm not sure what you mean by finite granularity. There is no "grid", space is continuous, the planck length and the fact that push on each other doesn't really factor in. By virtue of space being continuous and particles being finite, means you can configure stuff in infinite ways.
Edit: Not quoting you with the reference to a grid. I know that's not what you mean.
I'm not sure what you mean by finite granularity.
Are you aware of the plank length? It's the distance less than which which we can no longer determine if 2 things are any closer.
Not quoting you with the reference to a grid.
Don't worry, I understand.
So far nothing in the universe has shown to be infinite, hence any material representation of Gabriel's Horn can be painted since paint has a thickness.
The Plank length is the shortest possible distance between two material points. Though at that scale even vacuum is tempestuous.
Are you suggesting gayness is measured in number of humans?
No, but each individual human is assigned identically one gayness value, therefore the number of values we must sort is equal to the number of living humans
But the possible number of outcomes is not limited by the subset of living humans. While we may have a currently highest number that doesn’t mean it IS the highest possible, nor that there is exactly one of them.
While we may have a currently highest number that doesn’t mean it IS the highest possible
I would argue you can only be gay if you're alive, so you only need to compare living people, the theoretical maximum doesn't matter, only the actual maximum of a finite number.
nor that there is exactly one of them.
Agreed. It might be a shared gold medal.
It is true that the gayest person currently alive, the gayest person ever in history, and the gayest person who could possibly exist may well exhibit three different levels of gayness; however, I believe that, were one sufficiently determined, it would be possible to find all three.
I'd argue each of has a gay expression, Gayness can absolutely change in accordance with time.
Obviously not
Find the local maximum by taking the derivative:
dgay dt