How can inifinity exist?

D.P. said:
when you write down the number one hundred do yo really write down 100 digits, or the three digits 1,0 and 0? When you write down 1 billion, do you draw 1 billion symbols or simply write the text "1 billion".
Infinity has a symbol, a sideways 8.

Problem solved.
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You are writing down "take 1 and add 1 for 9 iterations, then multiple that by 10". The only information in there is "1", the rest is instructions on what to do with it. You can add "infinite" zeros on the end but really it is just a function saying "multiple the number by the sum of ten 1s and loop".
 
kwerk said:
You are writing down "take 1 and add 1 for 9 iterations, then multiple that by 10". The only information in there is "1", the rest is instructions on what to do with it. You can add "infinite" zeros on the end but really it is just a function saying "multiple the number by the sum of ten 1s and loop".
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yes, exactly. That is what maths is.
Maths involves the manipulation of symbols.
 
Using infinity is bad form. Our more pedantic markers will knock you down for it.

The right way to represent say 1/(infinity) is to say the limit of (1/x) as x tends to infinity

Bloody pedantic maths supervisors :(
 
Morbius said:
And if you add ±∞ to the reals you get a set known as the extended reals.



Yup. Suppose there is a planet that has two moons. Now imagine an infinite number of these planets. The amount of planets and moons are both infinite, but there are twice as many moons as there are planets.
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True there are an infinite number of infinities but the example given of planets and moons are in fact the same infinity. This is because there exists a one-to-one mapping between the two set (a bijection) using proven by showing the is a an injective relationship (many to one) in both directions.

The infinity of the natural numbers (0,1,2,3,4 etc) and the infinity of the Reals (basically every decimal number) are different as no bijection exists between the two. From memory and this is pushing the memory of my uni days, the cardinality of the naturasl is N and cardinality of the reals is Aleph-0, which is a greater or 'bigger' infinity.

Enough geekiness for now.

Impster
 
Judgeneo said:
Using infinity is bad form. Our more pedantic markers will knock you down for it.

The right way to represent say 1/(infinity) is to say the limit of (1/x) as x tends to infinity

Bloody pedantic maths supervisors :(
Click to expand...



Ha ha ha ha. Red tick and a gold star.


------
 
Impy77 said:
True there are an infinite number of infinities but the example given of planets and moons are in fact the same infinity. This is because there exists a one-to-one mapping between the two set (a bijection) using proven by showing the is a an injective relationship (many to one) in both directions.

The infinity of the natural numbers (0,1,2,3,4 etc) and the infinity of the Reals (basically every decimal number) are different as no bijection exists between the two. From memory and this is pushing the memory of my uni days, the cardinality of the naturasl is N and cardinality of the reals is Aleph-0, which is a greater or 'bigger' infinity.

Enough geekiness for now.

Impster
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Almost right......

The cardinality of the Naturals (infact any countably infinite set) is aleph 0. If you assume the Continuum hypothesis, which is provably unprovable (in PA) then the cardinality of the reals is aleph 1.

mmm maths
 
Infinity is not a decimal number, and like imaginary numbers it can't be represented in the usual way. As it happens you can store infinity in just one extended ASCII character.

Imagine the largest number you can store, now add one, does that number not exist?
 
Ghosteh said:
No, because there wouldn't be enough sectors on every hard disk on earth to store all the zeros lol.
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He didn't say store, he said "list".

10 Print "1";
20 Print "0";
30 Goto 20

Would eventually "display" this number but you wouldn't be able to see it all on any screen at any one time (assuming sufficient energy is available to run a computer for the lenght of time it would take to display this number...i'm no mathematician but i'm pretty sure it would take more time than the universe has already existed for).

So...theoretically, yes. Practically, no.
 
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Greebo said:
I always remember the infinite hotel from school.

A hotel has an infinite amount of rooms and every room is occupied.

Q1 A new guest arrives. Can the hotel accomodate him?
Q2 Infinite bus tours arrives with an infinite number of passengers. Can the hotel accomodate them?

Answers to follow but its easy.;)
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No, all the infinite rooms are occupied so therefore if an occupied room = n(with person inside) the equation is as follows:

8 (on its side [and hereafter used as the infinity symbol]) x n(with person inside) - n(without person inside) = 8n(with person inside)

Hence no rooms are unoccupied, so even if 1 guest arrived (let alone infinity bus loads of people) he'd have to go to the next hotel, which was probably nicer anyway and has a heated swimming pool.

Alternatively divide it all by zero and they can at least share rooms with some of the other occupants.
 
If there are infinite rooms then wouldn't an additional room be available? Suppose they are all occupied. But then what's the point in the question?

Isn't that like saying if a carpark is full then you have nowhere to park the car. All a bit too simple? :s
 
iamdjdz said:
No, all the infinite rooms are occupied so therefore if an occupied room = n(with person inside) the equation is as follows:

8 (on its side [and hereafter used as the infinity symbol]) x n(with person inside) - n(without person inside) = 8n(with person inside)

Hence no rooms are unoccupied, so even if 1 guest arrived (let alone infinity bus loads of people) he'd have to go to the next hotel, which was probably nicer anyway and has a heated swimming pool.

Alternatively divide it all by zero and they can at least share rooms with some of the other occupants.
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You can't just use infinity in an equation like that though a the rules of algebra only work for real numbers.
Besides the problem has already been answered by Danny091
 
iamdjdz said:
No, all the infinite rooms are occupied so therefore if an occupied room = n(with person inside) the equation is as follows:

8 (on its side [and hereafter used as the infinity symbol]) x n(with person inside) - n(without person inside) = 8n(with person inside)

Hence no rooms are unoccupied, so even if 1 guest arrived (let alone infinity bus loads of people) he'd have to go to the next hotel, which was probably nicer anyway and has a heated swimming pool.

Alternatively divide it all by zero and they can at least share rooms with some of the other occupants.
Click to expand...

sigma said:
If there are infinite rooms then wouldn't an additional room be available? Suppose they are all occupied. But then what's the point in the question?

Isn't that like saying if a carpark is full then you have nowhere to park the car. All a bit too simple? :s
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Because you can have infinite sets which "fit" inside other infinite sets, the answer to both is yes.

1. Get the guest in room 1 to move to room 2, room 2 to room 3, etc. ALl the infinite guests will still have a room and room 1 will be free for the new guest.

2. Get room 1 to move into room 2, room 2 into room 4, etc. Then rooms 1, 3, 5, 7, etc will all be free. Since it's an infinite hotel, then the total of all the odd rooms is infinite as well so hence there is space for the infinite bus tours

;)
 
You guys are missing the point, the infinite hotel would probably be empty anyhow as the reviews on trip advisor would be full of people complaining about having to move rooms. :p
 
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