The Concept of Infinity

Buckle up, kids, 'cuz I'm about to detonate your brain



What do you make of this? In all honesty, mathematics wasn't exactly my forte back in high school, but why with this video didn't the manager just create Room ∞+1 for every guest that arrived at the hotel?

 

Instead of moving people into a different room, it could have easily been solved by that "∞+1" statement. For programming, this can be achieved something like this pseudo-code:

Code:

INT guest
INT room
FOREACH guest
room + 1
END

Mathmatics wasn't my strongest subject, but its easy to understand that the Infinite Hotel had poor logistics just by moving guests from one room to another to make room for more people. Instead, all he had to do was add +1 to the most recent occupied room. Since there is always "room for one more" and construction never has to happen in order to do this (because "magic" or "science"), it's easy to figure out that it should be room + 1 and not "3^7" etc to figure out what room to assign new guests. Because "room" is a variable, it has an infinite possibility to be any number and since the hotel isn't using real numbers and only using integers, the only problem he would encounter is running into a naming problem to which you have exhausted all known number names. What are we up to these days for number names, Googolplexian (10[10[10^100])? With all the people on the earth, I don't think we'll ever hit the Googol (10^100) mark so being able to name the number won't be a problem. So the closest estimated number to hit would be the 7.5 billion mark, right?

 

I think it's more along the lines of the fact that, since the rooms are infinite, and all the rooms at any given time are already taken, the "just go to the infinity plus n room" doesn't work, since infinity plus any number n is still the same infinity, and thus that room (and a million rooms after it) is already taken. The trick here that people seem to fall for, is that infinity isn't actually a number, but a concept.

Back in highschool, when I still liked maths, our class had a for-fun discussion about infinity, and its multiple types.
There was the countable infinity; that of integers.
Then on top of that, there was all the infinite decimal points between each infinite integer.
And on top of that, there was the complex numbers for each of those decimals. It's about here that my brain starts to hurt.

 

Ok so you guys are talking a little over my head, but in my opinion there is no way to make sense of this idea because at our very core we our selves are fionite. I believe that you your self must be Infiniti to grasp the concept but seeing as how we our selves are fionite and live in a plane that is based completely on the assumption that there is a beginning and an end to every thing and that all time and other forms of mesure are leniar we are physically and mentally UN able to grasp the concept. For this concept to be practical time would ha e to be nonleniar.

 

The entire concept in my opinion is just one gigantic paradox. It was around the time when the narrator started to discuss things other than whole numbers when I felt the need to grab the nearest container of Tylenol and down a couple of pills to soothe my headache

Not only do we have the number infinity using whole numbers, but also when it comes to fractions, decimals, pi, and other mathematical factors that, when discussed, my head starts to hurt more than a cartoon character having an anvil or a piano dropped on them from above.

 

FREEZE. PROCESSING ANSWER...

Now that I have finally gotten around to doing this, I will say something.

I find this idea quite simple. The video and the mathematicians just make it confusing.
Infinity is without capacity.
It is a term that is beyond count.
Uncountable.
No matter what the greatest number is, you can still count 1 past it. The same goes for its converse.
The hotel is like this line:

It is unending and continues on in both directions. It is unlimited. Another line of the same length (infinite) will fit on this infinite line. I find that having an infinite amount of ∞ is the same as just ∞. Multiplying the amount of ∞ is like trying to multiply with 0: nothing is going to happen. Unlimited is unlimited.
And why the new guests cannot simple walk their lazy @$$e$ up or down to that end of infinity for their room, rather than disturb and agitate an infinite number of guests, is way beyond me. And hotel room numbers, according to the video, have a size corresponding to their number, such as the rooms labeled as fraction. I would think that would simple be a label, not a size. And besides, there is an infinite amount of decimals between each number, so between each number is an infinite amount of rooms .(1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ∞-2)

Thankfully, We do not need to worry about this, since we have yet to construct a 1,000,000 capacity hotel.

To ponder this subject is moot. Our dimension/universe has not been equipped for or given this problem.
I will enjoy my finite life in my finite hotels with finite people coming to finite rooms in our finite world with finite cities and finite countries that have finite resources.

 

This video is idiotic.
"Countably infinite".
No, you're missing the point of infinite.
Infinite does not have a number. If it had a set number, it would not be infinite.
No matter what sort of math limbo you try to do, infinite is always infinite. All of this extra math is nonsensical and pointless because there is always a room for every person. Always. Without fail. Hence infinite.

This whole thing of "well he asked them to move down one room blah blah" again, nonsensical. He goes in whatever room, wherever, because infinite.

 

*Reaches far back to the maths part of my brain*
Okay guys, this is how this part you're having trouble with works.
Yes, infinity is infinite, but there ARE different kinds of infinity. You can't minus one infinity from another and expect to get zero, because they don't have a set value, so some infinities can be "bigger" than others.

Think of it this way. You've got the equation y = x. The plot goes in a nice straight line, with its upper limit being infinity.
Now, try again with y = x^2. The plot is a parabola and goes much quicker upwards than y = x, and its upper limit is also infinity.
Again for y = x^3, and you're going up even faster.
All these plots are assigned to go to infinity, but when some plots go much faster than others, can we really say that each infinity is the same?

 

Infinity is infinity. There is no concept of time to an infinite integer. It is infinite, was infinite, and always will be infinite. If you want to say "it takes x amount of time for infinity-A to reach infinity-B" then go right ahead.

But you would be wrong.
The word infinity already dictates its size - infinite. One infinite can not be less than another infinite at any given time because by being less that infinite is no longer infinite.
If the number is growing it is not infinite.
All infinite integers are the same size. Infinite.
I am having zero problems understanding this. But the concept of a finite infinity is stupid and wrong.

I think what you're having trouble with is comparing infinite to actual numbers.
It is not. Infinity is a concept.
You can not count infinity
You can not do math with infinity.
Rather than saying "it's like dividing by zero", I'd say it's more like trying to divide by The Art of War.

Using infinity as a mathematical integer is pointless and nonsensical.
It's a word, and a concept. Not a number. If you say it's a number, it's not infinite. A number has a finite end.

 

You have brain?
*smack*
*bad Core!*

So the idea is that :
UNLIMITED<UNLIMITED
Or
UNLIMITED>UNLIMITED
Because of the different amounts in infinity? Sorry, that makes less sense.

Take a square:

It is limited. It has borders. It is a square.

Take infinity:


It is unlimited. It has no limited value. It is infinite.

Take the square's limit. Its area is contained in that shape and form.
Now break it.
Break it now.
One side is missing.
It no longer is a square, neither is it limited in area. You cannot measure its area, for it is now limited.
This is infinity, the broken square.

How fast you generate infinity, is of no concern. It is simply going nowhere fast. Infinity is infinity. Unlimited is unlimited.
It is tantamount to trying to fill two infinity balloons at different rates of different rates. Sure, on might fill at a rate progressively faster than the other, but when there is no limit to capacity, there is no reason.
As stated a moment ago, just going nowhere fast.

 

Guys, please. This isn't something we're debating; it's mathematical fact that I'm explaining. I learned this stuff directly from people at uni who work with complex maths problems for a career.

 

So basically what you're saying is you're unwilling to listen to anybody else because you are certain what you are saying is fact

So don't post then.

 

The thing is, this isn't a topic that can really be debated here. At minimum, it'd be between career mathematicians. My first-year uni maths unit had a whole section on finding out whether equations head towards a number, or go off to infinity. AND that if one half of the equation diverges to infinity and the other to -infinity, you CANNOT say that the equation will go to zero, because of the different rates and kinds of infinity.

This is one of the things in life that isn't able to be discussed, because not all opinions are of equal weight. Infinity is a concept well-defined by mathematicians, who are the very people who work with it.
It's like average people deciding for themselves whether a bridge is safe despite engineers saying it's going to collapse.

 

I'm just coming in to say something about the bridge comment with engineers...

I would listen to the guy who was building the bridge over the guy who designed the blueprints to tell me if the bridge is structurally safe. guess it's a matter of opinion since my dad is a construction worker. That being said he also makes his own blueprints and reads them well. Long and short of he told me a bridge is going to fall I would take his word over the engineers. Simply because he knew how stable it was when he was putting it together.

 

Infinity is Infinity!!!!!! Stop arguing about a question that has a universally known and accepted answer!!!

 

*derp*
Whoops, sorry, didn't mean to sound hostile or aggressive. Just tried to state my thinking on the subject, my reasoning at the most basic/logical level, but must have forgotten to say that was just my idea and reasoning.

I can see in part how different infinities could take place though, when I think about different universes. If a universe is infinite, and expands faster than another, than I think I can see another rate of infinity.
Though when you say "upper limit being infinity" and infinity is not a limited thing:

Oh, well.
I kinda understand that I don't get the idea of understanding something understandable to some who get how it is understandable to be understood.

I guess it won't hurt to leave my thinking at that. I'll just leave that thinking and math work to God and an infinite amount of unfortunate angels who are tasked with running around getting infinite supplies of paper and sharpening infinite amounts of pencils in an infinite amount... ack! Over thinking again! People are just too finite to handle this, I think.

Just kicking around this subject for the fun of it, no real argument, since it is merely a concept and not a proven fact... or is it? [cue X Files theme song]

I would make a mean glare at you for questioning my goal in life, but it does make sense how you're dad would want to be certain about a project.
Just keep in mind: We drafters and engineers know what we are doing.



There, I think that's all I have to say, unless I tripped up and forgot something important.

 

It's not so much that I doubt the engineers about blueprints. But I would rather confirm how structurally sound something is for the time my father is alive. Mostly because he is one of the best construction workers in the area. That's really the only reason I would confirm it with him. He built a lot of crazy structures from schools to malls and hospitals. Know what I mean?

Good for you for wanting to be an engineer I suck at math. So I don't particularly wanna go into That field. I'm likely going to go into something more like mortuary science or surgeon tech. Just up my alley.

 

Well, not quite the engineer part for me (for now), though drafters work with these engineers. I (the drafter) will draw what the plan based on the engineer's info and see if it's sound in design. If for the New Golden Gate Bridge a 100' suspension cable is being used when a 1,000' suspension cable should be used, I walk up to the engineer and say:

I doubt that entails all of my work, but I guess I am a bit of a middleman, making the work presentable and sensible. Oh well, I still need to actually work the actual job or intern to get all the details straight.
Anyway, I've heard some stories from my instructor about the stuff he helped design, so I have an idea for how it goes and what you mean.
I just hope my work does not deal with infinities (though I noticed one that one of my CAD programs use lightyears as units for measurement).

As for what you plan on going into, sounds interesting.
If you can't help save 'em, you can figure out what killed 'em.

 

Mortuary science is more so just making people presentable for the funeral. I will know how they died though because I get the coroner reports and what not. But yeah they're both really good fields.