| Subject: I think |
Author:
Damoclese
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Date Posted: 09/10/04 10:22am
In reply to:
Duane
's message, "Tristam Understood" on 09/ 9/04 1:48am
>
>The set of days is countably infinite
>
>The set of years is countably infinite
>
>Therefore, the set of days is the same size (that size
>being "countably infinite") as the set of years.
I think it all depends on how you wish to stack it. Years contain days,(as you noted in some previous post) and so saying that is equivalent to saying day one corresponds to 365 days. (roughly) So, in year one (365 days) he writes about day one. (overlooking the fact that if someone is in an infinity, there really exists no such thing as a day one. Other questions spring to mind such as if you are in an infinity, why would you use an Earth method of counting the years?)
Clearly, one can see that this function is always going to leave behind more and more days that haven't been written about all the way to infinity, but what of the number of days he has to write? It's true that that particular number is infinite also, but there's a provision. He has to experience 365 days before he can write about a day. That means at any given point along the line, there are going to be more days left to write about as opposed to days already written.
So now that we know what the points are doing, lets talk about them. What happens to the points as they approach infinity? Well, the same relation holds and we could demonstrate for any point you'd cared to pick, there would be more days left to write about, infinitely so. There is never a point where the relation is broken. At infinity,what we're talking about is the duration of the points themselves. How much time do we have for these points to exist? Infinitely so. What is true of each and every point on the line? That the number of days written about is always smaller than days experienced.
Infinity isn't talking about the days and years as separate entities here; we're talking about given what we know to be true about the relationship, what's the amount of overall time do we have that this relationship holds steady? It continues to hold forever. As the line goes infinitely out, the points upon it hold fast to the rules.
As with any other mathematical function that goes to infinity, it's assumed that infinity means "this relationship goes on for as long as you care to take it" It isn't that the days and years both eventually reach a quantity known as infinity, because that'd be breaking the function into bits.
So, that's how I look at this thing. To me, it's more of a paradox because of the words.
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