How do you pronounce Chongqing? Chong Ching or Chong king? I hear both everywhere and it’s driving me nuts!
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Assuming you’re talking about Chinese pronunciation, then the former one is the correct way. “Ching”, depending on its tone, can be written and pronounced in numerous Chinese letters, like “青” (qīng, blue) “情” (qíng, affection) “請” (qǐng, please) or “慶” (qìng, celebrate). However, there isn’t such pronunciation as “king” in Chinese (at least in Mandarin, not sure about Cantonese), nor can it be written in any character.
Hope this info helps. 
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From what ive heard from people that speak the language its pronounced as chongching, with chongking being the english romanization
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@Euler13 sorry to bother, I had a question. The video below constructs a situation, where an infinite hotel runs out of rooms under certain circumstances. While it’s understandable that in the last case there can always be more strings, why would the hotel have “no more” rooms considering there can always be one more room?
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An easy one for Friday evening, eh? 
I’ll give it a go, but I’ll probably create more confusion than clarity.
The issue is to do with what we call denumerability. If a set of objects (like room numbers) are denumerable, then it means that each element can be put in a one-to-one mapping with the set of counting numbers. We call these types of numbers countably infinite.
So when we ask someone in room n to go to room n+1 (as in the first case) or to room 2n (in the second case), each occupier of the original room has a clearly defined place to go. No one will be confused or uncertain which room they are being moved to.
In the last case, it turns out that the infinite set of binary strings (made of A’s and B’s or 0’s and 1’s) are not denumerable. Meaning there is no system that would allowing a clear mapping between, say, a particular string and a room number.
In other words, there are degrees of infinity. The smallest measure of infinity is the counting numbers and the “size” (cardinality) of this set is designated as aleph_0. The real numbers (or infinite set of binary strings) have a larger measure of infinity and it is designated as “c”; not to be confused with the speed of light!
Simply put, the size of the hotel is countably infinite. The cardinality of the last bus is not.
If something is not clear, please ask and I’ll try to explain. However, it has been wisely said that the infinite is quite literally more than we can ever understand.
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Thanks for the response!
The wise were right tbh… I’ll ask if something was still unclear, which is probably the case 
but first things first I have to put a bit of time into understanding this one.
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Doesn’t it all depend on the interpretation of “infinite?” I mean, infinite really only means that the finite boundary of the subject is not known, it doesn’t necessarily mean that there isn’t one, right? So one can theoretically declare something infinite as having finite possibilities, just that it is impractical, implausible, or impossible to actually count out the numbers and find where the finite boundary is, making it both infinite and finite simultaneously. Or am I off? It’s been a while since I considered such mechanics and the stuff in my head on the subject had collected dust.
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Literally the word infinite means not finite - not countable. However, the term infinite has many connotations. One way in which mathematicians try to (formally) make sense of the infinite is in the area of set theory. This work is primarily credited to the brilliant 19th century German mathematician, Georg Cantor. The notion of something being countably infinite is very helpful in understanding other concepts in mathematics. However, as Cantor showed, even this measure of infinity is incapable of measuring the size of other sets. It’s in this domain that the popularised paradox of Hilbert’s hotel emerges; the argument was introduced to the world by the incredible German mathematician, David Hilbert, in a lecture he gave the early 20th century.
@Hichkas: If it’s the concept of having a larger degree of infinity that you’re struggling with, I can attempt to explain.
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If 47 drops an infinite number of duckers, would duckers still be infinite? No. Because not everything is a ducker. 
Looks at 47 under a microscope at the planck scale, sees that he’s made of ducker at this level. Yet, the empty space between duckers is NOT ducker. 
…
As for the hotels Rms. I wonder what the case would be if you had a Rm -1, and infinite going the other way? With the starting limit of a Rm 1 you have to expand from there. Then let’s say you have floors going up infinitely. Still unlimited but “limited”? Then lets have a basement with -1st floor and Infinite lower levels. Still “limited”? Then hallways (see where this is going? X, Y, and Z dimensions) going towards the back and of the building… Then why not from the front of the building?
So then you have infinite Rms going both left and right, on each infinite floor going up and down, and infinite hallways on each floor from the center going to the back and front.
Now could this infinite party bus be accommodated? Do we have to go to a 4th spacial dimension? Why stop there?
Sounds like a Front Desk person’s version of hell. Not just any hotel hell…
There’d be a random number of Rms calling down complaining about the TV not working, how do you turn on the heat or AC, the toilet is clogged, there’s a stain on the bed-sheet, I’ve locked myself out of my Rm, I’ve lost my Rm key or got it too close to my cell phone, have you seen my significant other? Their car is out front and I can’t seem to reach them. The people next door are being too loud, the smoke alarm is going off, may I get a wake-up call? and on and on…
Getting a headache just thinking about it.
I’m not asking for clarification on anything, I just let my mind run wild there for a while.
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It’s certainly not a place you’d want to work! 
Incredible as it may sound, an infinite number of infinities - like an infinite number of corridors, each with an infinite number of rooms - is still countably infinite. From this it seems almost beyond comprehension to think that there is a measure of infinity greater than this. Yet there is! And in all likelihood there are infinities beyond infinities.
On a related note, a lovely mind game I like to play with my classes - I am so cruel! (Any mathematicians reading this, please note I’m using “how many” in a very loose sense.)
Me: How many positive integers are there?
Class: An infinite number.
Me: Okay, so how many even numbers are there?
Class: An infinite!
Me: Right. How many odd numbers?
Class: Still an infinite number.
Me: Okay, if I wrote out all the counting numbers and crossed off all the odd numbers, what would be left behind?
Class: All of the even numbers.
Me: Very good. So what you’re saying is that starting with an infinite set of numbers (1, 2, 3, …), I can remove an infinite number of them (all the odd numbers), and rather than be left with nothing there’d still remain an infinite set of numbers (the even numbers)? Yeah, that makes sense.
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As an instance of infinite being greater than infinite, can we go for prime numbers and odd numbers? Both infinite, but subtracting odd from prime leads to (only) 2, where the opposite case is still infinite.
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But there are odd numbers which are not prime, so it leads to negative infinite, not 2. 
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What you’re suggesting is at the heart of the first case in the Hilbert hotel paradox. You could say, “Remove all the numbers greater than 1 from the set of counting numbers. Here you have removed an infinite set of numbers from an infinite set of numbers and are left with one value; that is, infinite take away infinite appears to be 1 or any finite value you choose, k, by removing numbers greater than k.”
The point of the paradox is to show that you can’t do arithmetic with the infinite. Infinity is not a number, it represents a concept of something being beyond measure. Many paradoxes are based on the misconception that the infinite is a value you can apply the laws of arithmetic to.
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Ok clever guy, then tell me. There is a varying amount of natural numbers between prime numbers. Can this amount also be infinite?
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Not clever, it’s just my craft. But even after many years my mathematical knowledge is quite limited. Like an experienced chef who specialises in working with particular foods.
In answer to your question, no, the amount cannot be infinite. It can, however, be as large as you want.
We know that n! = n * (n - 1) * (n - 2) * … 3 * 2 * 1 is divisible by all the integers from 1 to n.
So n! + 2 is divisible by 2, n! + 3 is divisible by 3, and so on.
That is, none of the numbers n! + 2, n! + 3, … , n! + n are prime.
Hence for a finite value, n, we can guarantee to find a consecutive set of n - 1 composite integers. But as n is a number it can only be finite, so although there can be an arbitrarily large run of composites between any two primes, it cannot be infinite.
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Alas! You would be able to accommodate those passengers in this case.
You could assign all the guests in room X to the room 2^X; so they go to rooms 2, 4, 8, 16, 32, et cetera.
Each bus is allocated a prime number, such that bus Y is allocated the the (Y+1)th prime: p_(y+1); i.e. bus 1 is given 3, bus 2 is given 5, bus 3 is given 7, and so on.
Each passenger, Z, on the bus allocated room p_(y+1)^Z. For example, bus with prime 3 go to rooms 3, 9, 27, 81, 243, and so on.
Each person will be allocated a unique room.
However, we notice that no one is in, say, room 6 because it is not the power of any prime. Similarly, rooms 10, 12, 14, 15, et cetera.
In other words, we had a hotel with infinity many rooms that was full. After accommodating an infinite infinity of passengers we now have infinitely many unoccupied rooms.
You gotta love the infinite! 
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But is that hotel profitable if you have to give the staff an infinite number of money?
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Damned, I haven’t touch this stuff in years.
I know there is an example that can be easily be imagined where it’s impossible.
I will try to find my old notes.
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You’re spot on about the set of real numbers. In the video they use a really nice example, showing if a bus containing infinitely many passengers with names made of infinitely many binary strings: ABAAA…, ABBAAB…, and so on, then like the real numbers you could not accommodate this infinity of passengers.
I hope everyone will pardon the deletion and repost of my two previous posts but they were inaccurate in certain place.
@Euler13 I trust you to verify, if you want. (I notably previously mixed rational, real, and complex numbers, it’s been a while)
@Urben The best example of two very different set of infinity is :
- N set, the natural set (ie “full numbers” used for counting, 1 2 3 4 5…) : there is obviously an infinity of them
- Q set, the rational set (ie decimals 0,1 0,01 0,001…) : also an infinity of them, but well there is an infinity of them more than the natural one since there is a infinity of them between each natural number.
Both are infinite. One is seemingly larger, but both are countable and in the end as.
Even more both can be expressed with the other.
@Hichkas Something else you could have for the hotel is to imagine it incrementaly.
Imagine the following :
- You have an hotel with an infinity of room.
- Arrive an infinity of clients
- The hotel is full
Suddenly an new client arrives, can you have more than the infinity already here ? yes
- you wake every client and ask them to go to the next room
- the client in room 1 goes to room 2, the client in room 2 goes to room 3, the client in rrom 3 goes to 4, …
- you give the key to room 1 now unoccupied to the new client
- the hotel is full, all client are served
So infinity +1 is still the same infinity
Even more suddenly an infinity of clients arrive, can you have that much more ? yes
- you wake every client and ask them to go to the room with twice the number
- the client in room 1 goes to room 2, the client in room 2 goes to room 4, the client in room 3 goes to 6, …
- every client is in an even room
- you give the new clients the uneven rooms, there is an infinity of them
- the hotel is full, all clients are served
So two time the infinity is still the same infinity
An infinity of bus arrive with an infinity of passengers each, can you have that much more ? yes
- you do a double entry table with at the top the bus number and on the side the passenger number
- you fill it in diagonal for an easy match for everyone
| - || Bus 1 |Bus 2|Bus 3| Bus 4 |Bus 5|…|
|—|—|—|—|—|—|—|—|—|—|
| P1 ||1|3|6|10|15|…|
| P2 ||2|5|9|14|20|…|
| P3 ||4|8|13|19|26|…|
| P4 ||7|12|18|25|33|…|
| P5 ||11|17|24|32|41|…|
|…||…|…|…|…|…|…|…|…|
- the hotel is full, all the clients are served
An infinity of infinity is still the same infinity
The importance in set of infinity is to know if you can express one with an other.
In other term can we transform the numbers in the set with mathematics into a number that also is in the same set.
Can we transfer a number in another number place, a client in another room
If so they are as big/identical, if not one is larger than the other.
(I just realised I might have just resaid what was told in the video, I can’t watch it now)
But now is when things start to be tricky.
As I said, the important part is to know if each set of infinity can be expressed from another one.
In the previous examples, in mathematics all of them are part of the Q set. The rational set.
The definition of the Q set is any numbers that can be expressed as a fraction of two natural number
- 1 is a rational number.
- 0.5 is a rational number because it also is 1 / 2
- minus 2.27465892247 is a rational number because it’s also -53872153 / 23683618
- …
But then you have numbers like pi or the square root of 2.
They are part of the R set, the real set.
It’s definition is that it’s any numbers. Like that’s it. Any numbers that are in reality (hence the name). (alright I simplify, there is obviously more, much more, because mathematicians are a bunch of rude people, but that will be enough for us here)
As a consequence they also includes numbers that cannot express themself as a fraction of two natural numbers.
- for the funny anecdote, in ancient greece there once was a sect
- this sect was one of mathematicians (yes, I know)
- it was called the pythagorian
- the largest tenet of the sect was the beauty of the world and how everything can be expressed through fraction
- the most holy number was what we now call pi, because it was the beautifull number that could express through a fraction a circle.
- they then discovered that pi itself could not be expressed by a fraction
- it did not end well
- madness
- like murder over it to hide the shame kind of madness
Remember when I said the importance is if that the infinity set need to be capable of expressing themself with another ?
Well, that’s it.
In the metaphor of the hotel, you have a rational number of room, so if a real number of clients arrive then you won’t be able to accomodate them all.
Because there is no way to transform all the possibility of the real set into the rational set.
You will always have some left, all the one that are not a fraction.
You would be capable to do the reverse though.
An hotel with a real number of room, some named pi, some other name squareroot of 2, some just named 42.
A list of client named after rational number.
With a lot of room to spare
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