Please do not limit your understanding of an infinite collection to any particular class.
In order to avoid this limitation please think about a collection where the number of classes is the same as the number of the elements.
By this generalization of the concept of collection, a concept like "missing" has no meaning.
Good, I'm getting back to what I thought you meant by an "infinite collection" earlier. "Infinite" meaning it can never be complete, because the items to be collected have no common class. A collection of Beetle's record albums is finite, because it's merely of a single class of items. A record can be missing from the collection, and the collector may pay a premium price to fill that gap.
But when speaking of the infinite, all classes and groups must be abandoned.
Each item is a class by itself, a totally unique thing.
The collection is a grab bag of whatever I chuck into it, and since the contents aren't defined by common classes, the collecting isn't missing any item, while at the same time, no item can be excluded from it.
Nothing missing and nothing excluded, hence Doron Infinite.
Now if the Real Numbers are thought of as instances of a class of objects, a class exclusion takes place, a limitation, even if it's claimed that the the items in the class are 'infinite." Class prevents there being the open inclusion you mean for the Infinite.
Organic Numbers are each one a unique thing, at least in their non-local or parallel aspect. If you take them collectively, there is no defined class that prevents other unique individual numbers from being included, hence they are an infinite, but not complete, collection.
"Infinite" here means open and nonexclusive.
Mathematics for most everyone here is a manipulation of quantities of defined classes. Every mathematician asks you for definitions based on class identity. They also ask you for mathematical formulas.
But it's like their asking you for something unnatural.
You feel this this class based thinking limiting and tyrannical.
It's not the way you naturally think.
What strange animals we are to you.
And I must agree with you that analytical thinking is an inappropriate framework for questions of ethics and interpersonal relations.
All of us here experience and use non-linear thinking in various aspects of our lives.
But no one else I've read has thought to systematize non-linear thinking in a kind of mathematical-like framework.
I doubt non-linear thinking can be so formulaic. Care, respect, empathy aren't matters of calculation for me. And I don't feel I need to regard numbers as individuals instead of quantities to overcome my prejudices.
