dilberts hotel

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killing raven sun
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Re: dilberts hotel

Post by killing raven sun » Sat Jan 05, 2019 5:03 am

jliat wrote:
Fri Jan 04, 2019 6:22 am
killing raven sun wrote:
Fri Jan 04, 2019 5:43 am
start at infinity
:doh:
jliat wrote:
Sat Dec 29, 2018 3:11 am
Mathematics is a priori. Triangles don't get to have three sides... once you have the concept of the hotel, its being able to accommodate an infinite number of guests is part of the concept. Likewise you don't argue that a triangle has three sides by inspecting triangles... and building up evidence...
["infinity"...15, 14, 12, 11]

basic logic

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jliat
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Re: dilberts hotel

Post by jliat » Sat Jan 05, 2019 5:55 am

killing raven sun wrote:
Sat Jan 05, 2019 5:03 am
jliat wrote:
Fri Jan 04, 2019 6:22 am
killing raven sun wrote:
Fri Jan 04, 2019 5:43 am
start at infinity
:doh:
jliat wrote:
Sat Dec 29, 2018 3:11 am
Mathematics is a priori. Triangles don't get to have three sides... once you have the concept of the hotel, its being able to accommodate an infinite number of guests is part of the concept. Likewise you don't argue that a triangle has three sides by inspecting triangles... and building up evidence...
["infinity"...15, 14, 12, 11]

basic logic

Sure - you started at infinity - as you suggested - and counted down to "prove" you didnt start at infinity... = contradiction, basic logic..

You stated the set missing 13 but consisting of all the even numbers - infinite
and all odd without 13 - also infinite could be shown to not be infinite by counting down from infinity! But because 13 was missing it wasn't infinite... :doh:

Think about it, counting down from infinity you think the first number you count to is finite, i.e. its a number 1 less than infinity.
But its obvious you can never get to infinity by adding 1 to a finite number, you get a finite number 1 larger...... like wise you can never get to a finite number by subtracting a finite number from infinity.

So you are Trolling - the 'best' explanation …

killing raven sun
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Re: dilberts hotel

Post by killing raven sun » Sat Jan 05, 2019 6:18 am

jliat wrote:
Sat Jan 05, 2019 5:55 am
Sure - you started at infinity - as you suggested - and counted down to "prove" you didnt start at infinity... = contradiction, basic logic..
no, i started at "an infinite whole number", remember infinity isnt a value, then i counted down to where the set becomes non infinite, the location where "13" has to be for the set to contain "all whole numbers", thereby proving that the set is not infinite

its plainly obvious you are the troll james, you dont have any purpose at this board but to be my dog

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jliat
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Re: dilberts hotel

Post by jliat » Sat Jan 05, 2019 6:24 am

killing raven sun wrote:
Sat Jan 05, 2019 6:18 am

, i started at "an infinite whole number",
Subtracted 1 and got a finite whole number 1 less than an infinite whole number.... (how on earth you can get to an an infinite whole number - not withstanding.. ) :chin:

Anyway you made Tim LOL.

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Re: dilberts hotel

Post by xdugef » Sat Jan 05, 2019 6:34 am

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killing raven sun
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Re: dilberts hotel

Post by killing raven sun » Sat Jan 05, 2019 6:48 am

jliat wrote:
Sat Jan 05, 2019 6:24 am
killing raven sun wrote:
Sat Jan 05, 2019 6:18 am

, i started at "an infinite whole number",
Subtracted 1 and got a finite whole number 1 less than an infinite whole number.... (how on earth you can get to an an infinite whole number - not withstanding.. ) :chin:
no, you are still thinking infinity is a value, its not, you can continue to count into infinity in a set of whole numbers that is missing "13" but the set itself is not infinite, by definitiion it lacks an element, therefore not infinite

i see you are a fan of cantor, thats your problem

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Re: dilberts hotel

Post by xdugef » Sat Jan 05, 2019 6:56 am

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jliat
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Re: dilberts hotel

Post by jliat » Sat Jan 05, 2019 8:22 am

killing raven sun wrote:
Sat Jan 05, 2019 6:48 am
jliat wrote:
Sat Jan 05, 2019 6:24 am
killing raven sun wrote:
Sat Jan 05, 2019 6:18 am

, i started at "an infinite whole number",
Subtracted 1 and got a finite whole number 1 less than an infinite whole number.... (how on earth you can get to an an infinite whole number - not withstanding.. ) :chin:
no, you are still thinking infinity is a value, its not, you can continue to count into infinity in a set of whole numbers that is missing "13" but the set itself is not infinite, by definitiion it lacks an element, therefore not infinite

i see you are a fan of cantor, thats your problem

Well Cantor invented set theory, which is quite foundational, and you are talking about sets... for starters, there are many types of sets, you conflate the set of whole numbers - which is infinite, with the set of whole numbers less 13, which is also infinite, though not the 'complete' set of all whole numbers. Likewise the set of primes is infinite, as is the set of primes which are odd. Though the latter is not complete.


In short "complete" all the items characteristic of a set, does not entail infinity. A set of playing cards for instance, finite and complete, or finite and missing a card.

The set of whole numbers starting at Googolplex is not complete but still infinite, and of the same size as any other Alef zero set.

And yes infinity isnt a value, so how can you count down from it! (Though it is countable by bijection)

So by definition the number of rooms in a Hilbert Hotel missing 13 has not the complete set of integers yet is still infinite. As is a Hotel with just even numbered rooms... You even said yourself the set of even or odd numbers is infinite.


Youve also missed out zero and negative numbers... "whole numbers"

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Re: dilberts hotel

Post by xdugef » Sat Jan 05, 2019 8:37 am

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jliat
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Re: dilberts hotel

Post by jliat » Sun Jan 06, 2019 2:05 am

So you are saying that all the odd numbers are infinite despite not having any of the even numbers.
killing raven sun wrote:
Sat Dec 29, 2018 8:29 am

sure, why not? its an infinite subset of "numbers"
So if you have a set of all the whole numbers and remove 13 you say its no longer infinite BUT

if you have a set of all the whole numbers and remove all the even numbers you have an infinite set of odd numbers..

killing raven sun wrote:
Sat Dec 29, 2018 8:29 am

"some infinities are bigger than others" :lol:

" Strange but True: Infinity Comes in Different Sizes... In fact, Cantor showed, there are more real numbers packed in between zero and one than there are numbers in the entire range of naturals (whole numbers..)."

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Re: dilberts hotel

Post by jliat » Sun Jan 06, 2019 2:45 am

The set of natural numbers is an infinite set. This kind of infinity is, by definition, called countable infinity. All sets that can be put into a bijective relation to the natural numbers are said to have this kind of infinity. This is also expressed by saying that the cardinal number of the set is aleph-naught (ℵ0).

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number). Included within the irrationals are the transcendental numbers, such as π (3.14159265...). In addition to measuring distance, real numbers can be used to measure quantities such as time, mass, energy, velocity, and many more. ... The reals are uncountable; that is: while both the set of all natural numbers and the set of all real numbers are infinite sets, there can be no one-to-one function from the real numbers to the natural numbers:

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jliat
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Re: dilberts hotel

Post by jliat » Sun Jan 06, 2019 5:08 am

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killing raven sun
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Re: dilberts hotel

Post by killing raven sun » Sun Jan 06, 2019 5:51 am

jliat wrote:
Sat Jan 05, 2019 8:22 am
Well Cantor invented set theory, which is quite foundational, and you are talking about sets... for starters, there are many types of sets, you conflate the set of whole numbers - which is infinite, with the set of whole numbers less 13, which is also infinite, though not the 'complete' set of all whole numbers.
no, the set without "13" is finite, the set is [whole numbers - "13"], being able to count infinitely in either direction away from the missing "13" does not make the set infinite or complete, once again you try to understand infinity as a value, its not

a whole set which has an element removed is incomplete and therefore finite
jliat wrote:
Sat Jan 05, 2019 8:22 am
So by definition the number of rooms in a Hilbert Hotel missing 13 has not the complete set of integers yet is still infinite.
correct, the set [rooms] is still infinite because you have not removed a room, its elements are all intact, the set of room numbers though is now missing one, so the room number set is not infinite

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Re: dilberts hotel

Post by killing raven sun » Sun Jan 06, 2019 6:01 am

cantor was a mathturbator
In 1888, Cantor published his correspondence with several philosophers on the philosophical implications of his set theory. In an extensive attempt to persuade other Christian thinkers and authorities to adopt his views, Cantor had corresponded with Christian philosophers such as Tilman Pesch and Joseph Hontheim, as well as theologians such as Cardinal Johann Baptist Franzelin, who once replied by equating the theory of transfinite numbers with pantheism. Cantor even sent one letter directly to Pope Leo XIII himself, and addressed several pamphlets to him.

Cantor's philosophy on the nature of numbers led him to affirm a belief in the freedom of mathematics to posit and prove concepts apart from the realm of physical phenomena, as expressions within an internal reality. The only restrictions on this metaphysical system are that all mathematical concepts must be devoid of internal contradiction, and that they follow from existing definitions, axioms, and theorems. This belief is summarized in his assertion that "the essence of mathematics is its freedom." These ideas parallel those of Edmund Husserl, whom Cantor had met in Halle.

Meanwhile, Cantor himself was fiercely opposed to infinitesimals, describing them as both an "abomination" and "the cholera bacillus of mathematics".

Cantor's 1883 paper reveals that he was well aware of the opposition his ideas were encountering: "... I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers."

Hence he devotes much space to justifying his earlier work, asserting that mathematical concepts may be freely introduced as long as they are free of contradiction and defined in terms of previously accepted concepts.
math is the polar opposite of metaphysical freedom, cantor was an idiot, and so are his students

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jliat
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Re: dilberts hotel

Post by jliat » Sun Jan 06, 2019 6:03 am

killing raven sun wrote:
Sun Jan 06, 2019 5:51 am

correct, the set [rooms] is still infinite because you have not removed a room, its elements are all intact, the set of room numbers though is now missing one, so the room number set is not infinite
So the set of whole numbers with all the even numbers removed is acording to the above not infinite, yet elsewhere you say the set of odd numbers is infinite, you contradict yourself. In fact you can subtract any finite number from an infinite set, it remains infinite.

You also have implied that infinity is only one element more than a finite number. Again clearly not true.

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