| Subject: Thoughts |
Author:
Damoclese
|
[
Next Thread |
Previous Thread |
Next Message |
Previous Message
]
Date Posted: 05/26/04 9:17pm
In reply to:
Duane
's message, "Wade was right (sort of)" on 05/25/04 11:03am
Based on how I'm understanding your reply, here are my thoughts. Let me know if something seems fundamentally wrong. This isn't the easiest material to mentally manipulate; less so because there are so many ways to do it.
>
>Take the empty set - now add one element. There's a
>day, so he spends 365 more days writing about it. At
>the end of that year, as we've added individual
>elements to the set, we end up with 366 individual
>elements.
One of many problems with this whole thing is the ambiguousness of the definitions with which we are dealing. Here, the problem is figuring out whether or not day one should be considered as part of the same set or whether it should constitute a second set of 365 days.
In other words, if day one only corresponds to 365 days to write it, I'm not sure where that first day belongs.(e.g. tacked on to that first 365 days or 365 days FROM it)I'm not sure where to begin counting either. It's all very vague relying on intuitive notions of time.
However, if those things were cleared up sufficiently for me, I'd say this looks to be a valid objection to the one to one correspondence premise, at least for the sets in this argument.
>
>
>The 1 to 1 correspondence is not true for any finite
>subset of natural numbers, and I claim we may state
>that it is untrue for an infinite set of natural
>numbers.
This gets into very hairy territory. Based on Cantor's work between rational numbers and natural numbers and organizing infinite sets of them into one to one correspondences, I'm not sure that it's unreasonable to assume that two natural sets of infinite number can be placed in a one to one correspondence with one another. In this problem, the main issue that I see is that we don't know where to start placing things into a one to one correspondence, or what the cut-offs are. (i.e. days flow into years by definition)
>
>I think that your premise appears to be true,
>intuitively, for the infinite set (infinity / infinity
>= 1), but that's just illustrating an interesting
>property of infinity, and ignores the nature of this
>particular set (as explained above).
I really have issues with dividing infinity by infinity in the first place. In a mathematical sense where infinity has a strict definition, and infinities of different magnitudes are distinguished from one another, I think this has relevance and application. Otherwise, here I'm not sure that it does because I'm not sure infinity has to follow the rules that other numbers do such as one divided by one because infinity, by definition, is not a number.
Those are my thoughts for now.
[
Next Thread |
Previous Thread |
Next Message |
Previous Message
]
| |
Feedback: 