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Michael19682
Guest
If the sequence is 3, 4, and 7 he moves guest 1 into 4, guest 2 into 9, and guest 3 into room 17? and so on down the line? Y or N?
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Michael19682
Guest
That makes time a relevant variable, ie. “when the x new guests arrive”. In other words, he has to wait for infinity and if the number generator stalls, he is business is on hold permanently. This brings philosophy into the discussion and not just set theory. That was my whole point. The proprietor can never have a neat set of descriptive functions to describe a randomly generated number like Pi, which in practical reality hinges on the accuracy of a measured circumference and a measured diameter for “quality assurance standards” of each Pi.
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Michael19682
Guest
The video and you claimed instantaneous assumption of arrivals. You have just contradicted the video and yourself by saying “when”. End of argument for me.
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hecd2
Guest
Time is not a relevant variable. The proprietor can always accomodate more guests whenever they arrive. Pi is not defined by measured values nor is it random. Since pi is a transcendental number and therefore not a member of any countably infinite set, it is quite irrelevant to any discussion of Hilbert’s hotel which is confined to countably infinite sets. Are you sure you have enough of a mathematical background to discuss this sensibly?
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hecd2
Guest
What video? Time is irrelevant because whether the new guests arrive simultaneously or sequentially they can be accomodated. You have not stated unambiguously what your point is.
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Rhubarb
Guest
You’re picking at a part of the thought experiment that is just for rhetoric’s sake. It’s like trying to answer the Trolley Problem by coming up with some clever way to save the people on both tracks. You’re missing the point entirely.
Gah! How did I get dragged back in. I already washed my hands of it…
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Michael19682
Guest
They cannot be accommodated if their is no single rule of shift arrangement. TO be instantaneously assumed, or taken, by the Hotel, there must exist a single rule of shift for the proprietor to use in moving his guests around. I gave you an example, but you exclude it on the grounds of transcendentalism. I say that in order to apply the mathematical model of the Hotel to the situation of the Universe’s beginning you NEED transcendentalism. The fact that the Hotel is unequipped to handle a transcendental number is proof that it cannot satisfactorily provide proof for the problem of the Universe’s beginning.
The piece wise function analog that you declined to accept was a similar problem.
if x>0 then f(x) = 3x^2 + 1;
if x<0 then f(x) = x^3
if x=0 then f(x) = x;
as you can see, there is no single function to describe the entire graph: ergo,
the graph be neither instantaneously described as a whole picture nor differentiated at all points with the use of the product rule and the same function for all uses of the product rule. This is so obvious it cannot be understated.
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Michael19682
Guest
The link to the video in the OP!
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Michael19682
Guest
To measure Pi you need a perfect circle and a diameter. That makes infinite numbers of Pi according to how perfect you draw the circle in question. It is called a solipsism when you use a term to define itself. You can not say C = Pi(d) and Pi = C/d without a preoperative measures of C and d, which came from drawings and real world precision.
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Michael19682
Guest
YES!
And since an irrational set cannot be ascertained infinitely, you call it transcendental and say the Hotel is not equipped for it; rather, those guests should go to an asylum
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hecd2
Guest
Not necessarily. Hilbert’s hotel is an illustration of the theorem that the union of countable sets is countable and if one or both of those sets is countably infinite then the union is countably infinite. I have humoured your requirement to accomodate guests who arrive together in contiguous rooms, but that is not part of the theorem (or indeed of its illustration in the form of Hilbert’s hotel)
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hecd2
Guest
Of course they can - as I have said the hotel is an illustration of the theorem that the union of countable sets is countable. There is no “rule of shift arrangement” required.
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No
Can you prove that?
I think you need to take that up with William Lane Craig. I have never made the claim that Hilbert’s hotel provides proof of the finite or eternal past existence of the Universe, but Craig claims that it shows that the Universe cannot be past eternal. I happen not to agree with him.
I have no idea how quoting a non-analytic, non-infinitely differentiable function is relevant to Hilbert’s hotel, or indeed what relevance the product rule has to the example function you quoted.
If you are trying to say in a very non-mathematical way that the set of real numbers is not countable and so not equinumerous with a countably infinite set, then I agree with you. But Hilbert’s hotel is about countable sets.
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Michael19682
Guest
Thank you! I thought it was a reasonable requirement to ask because in the video again he keeps the original occupants no more than two rooms apart as opposed to trying to shove all the new arrivals in one “suite” as you have allowed for my experiment.
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hecd2
Guest
No. Pi is *defined *as the ratio of circumfrence to the diameter of a perfect Euclidean circle. To estimate the value of pi, it is not measured but can be calculated to arbitrary precision using various series expansions. However, I don’t really know what point your trying to make.
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Michael19682
Guest
It is a specialized illustration. I think it does require a shift rule, else it denigrates into absurdity.
Who would believe me anyway?
Thank you. We need not discuss further. But of course we can.
It’s rather like this. Say you know only word of a language (the presiding function of a very long section of a piece wise graph). Each time a person addresses you in that language, all you can say is ‘MO’, the one word you know. It matters not what they say, your response is in another word’s sense, instantaneous, without reflection (you simply apply the one formula you know to find f(x)) and that is that.
Now you learn a second word, OM, which they teach you after many many years (the function presiding over another section of the piece wise graph). Now every time someone addresses you, you must think of what to say, either MO or OM. Your answer, however irrelevant it is, is reflected upon, no longer instantaneous (because you are consciously matching up your function to the exact point on piece wise graph you are differentiating)!
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Michael19682
Guest
Arbitrary but not exact! Therefore its precision depends on the arbitrary depth of arbitrariness. In other words, a random precision based on a randomly generated depth of precision. Anything inexact-able is random. Except for God.
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thinkandmull
Guest
I have read a lot of really old math books. I am not interested in new definitions but the arguments. So far you have not given an argument, elegant or not, to prove that my position is wrong.
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thinkandmull
Guest
That irrational numbers are numbers is debatable too
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thinkandmull
Guest
Because causation is not accidental to time
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thinkandmull
Guest
homeschoolmath.net/teaching/rational-numbers-countable.php
I was homeschooled for years, but I didn’t get duped by this. “It’s just for positive fractions, but after you have these ordered, you could just slip each negative fraction after the corresponding positive one in the line, and place the zero leading the crowd.” That’s the error.
I was homeschooled for years, but I didn’t get duped by this. “It’s just for positive fractions, but after you have these ordered, you could just slip each negative fraction after the corresponding positive one in the line, and place the zero leading the crowd.” That’s the error.
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