Question About Hilbert's Hotel

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I’ll give you both showing off…I’ve cracked it. Answer me!
 
I said I understand some math. I got a very high SAT score for example

“Ad hominem argument, which does not address the question but attacks your opponent.”
“Can you give us an example of how the Gauss Bonnet theorem may be applied?”

There it goes. Another blatant contradiction
 
What is the Law of non-Contradiction as explained by 16 century Aristotelians?
 
Tomdstone said:
What have you cracked?
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I’ve undercut his premise that there is no way to establish infinity in the beginning!
He says the hotel proves a definite time for a beginning.
I proved that at the very least that the hotel does not prove no beginning; so the possibility remains to be proven that time had a beginning.
 
thinkandmull said:
I said I understand some math. I got a very high SAT score for example
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With such a high SAT score, why did you not pursue math further? Since you have this interest in math, it seems like it would be to your advantage to take a few college courses in math. This thread is not helping you understand what mathematicians are talking about.
 
Michael19682 said:
I’ve undercut his premise that there is no way to establish infinity in the beginning!
He says the hotel proves a definite time for a beginning.
I proved that at the very least that the hotel does not prove no beginning; so the possibility remains to be proven that time had a beginning.
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Can you state your discovered argument in a sentence? I myself agree with you but I want to see how you formulate it 🙂
 
Tomdstone said:
With such a high SAT score, why did you not pursue math further? Since you have this interest in math, it seems like it would be to your advantage to take a few college courses in math. This thread is not helping you understand what mathematicians are talking about.
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Fair enough 🙂
 
thinkandmull said:
Can you state your discovered argument in a sentence? I myself agree with you but I want to see how you formulate it 🙂
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The shift to the right of the room inhabitants assumes guests arrive one after another and keeps the hotel full, the latter being a condition of the puzzle: whereas if the guests must be taken in families of various size, a shift pattern must be used, to the end that this pattern can only be established with certainty for a finite number of guests because guests, who are taken in time, may always yet arrive, confounding the previous finite shift pattern. Like horizontal bar graphs stacked vertically in a single column,

++++++
++++++++
++++
+++++++++
+++
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You can never anticipate accurately the final item in the series because it arrives according to a pattern established randomly or otherwise in the mind of God.
Therefore, the shift, which is not static, can in no wise ever be determined and the hotel is a hub of confusion.
 
thinkandmull said:
So a thing cannot be a part of a whole and the whole at the same time.
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That’s very good reasoning, but once it gets left in the dust by the arrival of a new set member, it remains but a subset and not the full set.
 
thinkandmull said:
So a thing cannot be a part of a whole and the whole at the same time.
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Yes it can. You original (correct) example was between existence and non-existence. This second example is different and fails.

Are you, you? Yes you are. However, a few of your hairs can fall out, and you are still you. The new you is less (by a few hairs) than the old you. You are both part of the whole, and the whole at the same time. QED.

rossum
 
Another analogy consonant with the evangelist Johns own words.
If a book with sentences of vary lengths were the rooms of the hotel, and the shift was a photocopy of the these sentences,

Jn 21:25 There are also many other things that Jesus did, but if these were to be described individually, I do not think the whole world would contain the books that would be written
Therefore time had no beginning either, if and only if the hotel is needed to prove its beginning.
 
rossum said:
Yes it can. You original (correct) example was between existence and non-existence. This second example is different and fails.

Are you, you? Yes you are. However, a few of your hairs can fall out, and you are still you. The new you is less (by a few hairs) than the old you. You are both part of the whole, and the whole at the same time. QED.

rossum
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Not demonstrated at all. We get a totally new body in heaven:D and we are transformed like angels. The lord said it. Plus, the hotel takes numbers as an example.
 
Yeah, I’m going to step out of this now. I can handle willfully ignorant people. The concepts are very counter-intuitive. But this is turning venomous and there’s no reason for that.
 
Rhubarb said:
Yeah, I’m going to step out of this now. I can handle willfully ignorant people. The concepts are very counter-intuitive. But this is turning venomous and there’s no reason for that.
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I see Rhubarb’s point, but I also think that abstruse ideas like these are by implication “shared” and thus criticism of the other is like criticism of the self – a kind of self imposed trial by ordeal. Not nice, not truly self effacing, but not sinful as long as the discussion, or the life of it, remains ongoing.
 
There is a lot of Dunning-Kruger in this thread.

If thinkandmull is having trouble with the concept that the cardinality (the “size”) of the set of all odd numbers is the same as that of the natural numbers, what will he make of the proof that the set of all rational numbers (i.e. all numbers that can be expressed as the fraction of two natural numbers: 1/2, 3/7, 235673/256777654 are all rational numbers) is countably infinite and therefore the cardinality of that set is the same as the set of natural numbers, in spite of the fact that there are infinitely many rational numbers in the interval between any two rational numbers (the rational numbers are said to be dense rather than discrete). The same is true for the set of algebraic numbers (i.e. all numbers which can be expressed as the root of a finite, non-zero polynomial in one varable with rational coefficients). Indeed the cardinality of the set of rational numbers is the same as the cardinality of the set of any natural number raised to the power of all natural numbers (e.g. {13459^1, 13459^2, 13459^3 …} = {13459, 181144681, 243802621579 …} and this true no matter how big the base is.

Whereas the cardinality of the set of real numbers can be proven to be greater than these and that proof is ingenious and satisfying.

I am always amused and bemused in equal measure by people who casually consider some mathematical or scientific concept and who, failing to understand it, blame their misunderstanding on some elementary mistake that they believe has been made by the best minds who for decades have considered, accepted and enlarged on the concept, rather than blaming their misunderstanding on their own ignorance of the subject.
 
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