Ontology 1 - Infinity

Let's ease into the arguments with something that isn't too hard to digest


Let me start by addressing a few statements you made without a supporting argument. And I don't believe you can justify this.

You're making the assertion that traversing the infinite is impossible. You support this by observing that you cannot add to infinity.

This is a very common mistake people make when they think about infinity. They proceed to treat infinity as if it were a number. "infinity plus one equals infinity! You can't add to infinity."

But that is incorrect. You would do better to think of infinity as the cardinality of some set or other.

Let's, for example, look at the set of even numbers. This set contains the numbers 2, 4, 6, 8 etc.

Now it is clear that you can, of course, add to this set. You can add the number 1 to it. And 3. And 5. And so on and so forth.

The only thing you cannot say is that the resulting set, the set you get from adding the number 1 to the set of all even numbers, for example, has "more" elements than the original set. In other words, the cardinality of the set doesn't change. But rather than saying you cannot ADD to the set, you have to say that adding elements to the set will not change its cardinality.

In fact, even infinities come in hierarchies. Sets like the ones I described here are called COUNTABLE sets. This includes all sets like the natural numbers, all even numbers, all primes, all integers, and even all numbers that can be written as a fraction of two integers. All this means is that for each of those sets you can establish a one-to-one relationship between the members of that set and the members of any of the other sets that are infinite and countable.

I refer you to Cantor to learn more about infinities.

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[Ear4Beauty]

Interesting point and counterpoints which I am not sure I follow well. But ..

How do you "add" to anything without thinking what is being added to is in discreet unit/s ? (ie. numbered) . You can or cannot "add" to Inifinity ? That's the argument here ? My initial intuitive thought is to "add" is to encrease, period.

[rozeboosje]

@Ear4Beauty Well, you could "add" the set of even numbers to the set of odd numbers in order to produce the set of Natural numbers, for example. The funny thing is that you could, in one sense, argue that you have increased something. After all, there are numbers in the set of Natural numbers that don't exist in the set of odd or that of even numbers. But yet, all these sets are infinitely countable, and in that sense they are "equivalent" to each other, in cardinality at least.

[rozeboosje]

@Ear4Beauty This video may help: watch?v=TaW_E61vKFw

[attilitus]

it should be emphasized that the definition of an infinite set is a set which is not finite. Therefore, the fundamental quality of infinite sets is that it is a set S for which there does not exist a bijection between S and a section of the positive integers {1, ... , N} for some N.

[rozeboosje]

@attilitus True, but for what I'm discussing here it isn't that important.

[rozeboosje]

:-)

Don't give up.

[Randomninja47]

Lol it's okay. :)

I'm sure I could understand it if I didn't watch this while frustrated at my HW. Lol.

[rozeboosje]

A user named moistheman

Should be pronounced "mo is the man" but... Moist He-man!?!? LOL

I just realised that the guy has since removed all his video responses. Oh the humanity.

[RobertHaraldsen]

Who's Mo? Where?

[rozeboosje]

Thank you