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A Treatise on Infinity

52Cards

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“O God, I could be bounded in a nutshell and count myself a king of infinite space were it not that I have bad dreams.”
Shakespeare’s “Hamlet” (Act II, Scene II)

Infinity is the concept of forever. It is to extend on for eternity, never-ending. This concept, it cannot exist in reality, yet it thrives every day in today’s culture. Religion, theories of space and time, the size of the universe, all of these have the concept of infinity tied to them. But what is infinity really? Can anything actually be infinite? Infinity is a paradox unto itself, existing, yet nonexistent at the same time, and affects our lives in ways we cannot even begin to imagine.
Infinity cannot even begin to exist. This is due to the fact that if something starts, it has not existed forever in time, and therefore cannot be infinite. For something to be infinite, it must extend beyond the constraints of space and time. As we know now by the aid of scientific instruments, the universe is not infinite, but has boundaries that are constantly extending outwards, and have been since the birth of the universe. With this information, we know that any material object, or a lack of material, cannot extend to infinity unless it extends beyond the barriers of space. By the same token, time is not infinite. Time is the measure of the length of existence, or a section of an object’s existence. Since nothing existed before the creation of the universe, time began at the creation of the universe, and is therefore finite.
On the other hand, people cannot exist without this impossible idea. Every religion that has ever been practiced has a belief in some sort of power, whether it be a god, the human spirit, or some other medium, that has unlimited, or eternal, potential, power, or perfection. These religions have extended back to the first person capable of coherent thought. Only atheism, agnosticism, and humanism question the existence of eternity, and they are not actually religions because of their lack of a set of beliefs that all believers adhere to. Even without religion, we are compelled to believe in infinity. For example, the expanding universe theory which was presented earlier shows that the universe has definite boundaries. But what is outside these boundaries? Human nature makes it impossible for people to accept the concept of a finite existence. The fact of choice and chance also require us to believe in infinity. With choice, we make a decision that changes the universe, either subtly or distinctly. In chance, it is the possibility that something random will happen. These two ideas in conjunction force us to believe in the concept of infinity. It is the fact that anything can happen at any time, no matter how improbable it is, that forces us to accept infinity.
Infinity affects us every day in many different ways. One main influence of infinity is religion. As explained earlier, every religion has the concept of infinity embedded into it somehow. For many people, religion is the basis of beliefs, even before work and family. For example, modern Muslim terrorists sacrifice their lives for what they believe in. Also, every decision we make leads to a different reality, one of infinite possible realities. Every single thing a person does is based off of a choice, causing infinity to affect people every second of every day.
In conclusion, infinity cannot exist in reality. Even though it cannot exist, human beings require infinity as a base for their life. This presents an interesting paradox, for how can people survive on something that does not exist? We must explore this, in the words of Buzz Lightyear, “to infinity, and beyond!” The only question is, can we?


Note: This essay is not made to prove or disprove infinity. It is simply here to pose a question, not destroy beliefs. I try to make it clear that a material infinity cannot exist, but a nonmaterial infinity is necessary to exist. Please don't take this in the wrong way.
 
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1.) Numbers do not exist in reality. It is equally true and equally insignificant to note that the numbers 2 and 5 an 1115.314 do not exist in reality.

2.) An infinite number of things can be shown to exist in reality, however. Any real time interval features an infinite number of moments between its beginning and end, for example.

3.) Anyone that thinks "X has a beginning/end/both" implies necessarily that "X is not infinite" doesn't understand infinity. This includes you.

4.) Anyone that thinks an infinite set of consecutive elements cannot be wholly traversed in a finite time does not understand infinity. This also includes you.

5.) Anyone that thinks the universe has "edges" or "boundaries" is invited to supply evidence for their existence. Surely there are some people in Stockholm that would be greatly interested in such a revolutionary observation.
 
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Eudaimonist

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:æ: said:
2.) An infinite number of things can be shown to exist in reality, however. Any real time interval features an infinite number of moments between its beginning and end, for example.

That's only "true" mathematically. It isn't clear that one can subdivide moments infinitely in reality.

4.) Anyone that thinks an infinite set of consecutive elements cannot be wholly traversed in a finite time does not understand infinity.

I'd love to hear an explanation of how this is possible.
 
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My response to :ae:
Thank you for your concern. I will revise myself where necessary.

1.)Numbers do not exist in reality. It is equally true and equally insignificant to note that the numbers 2 and 5 an 1115.314 do not exist in reality.
THis is a very true statement. Numbers are an abstraction of the mind, as infinity is, therefore they can be infinite.
2.) An infinite number of things can be shown to exist in reality, however. Any real time interval features an infinite number of moments between its beginning and end, for example.
As Eudaimonist said, this is true mathematically, in the number world. As we have already proved that numbers are abstractions, then measurements, also contained in the subject of mathematics, are also abstractions. Therefore, it is true that we see an infinite amount of points in any given object or time interval, but how many times can we break this down? Break the object down to atoms? Farther? Greek philosophers gave atoms their name because it meant "uncuttable." We have proved the existence of subatomic particles today, but when will we reach that uncuttable point?
3.)Anyone that thinks "X has a beginning/end/both" implies necessarily that "X is not infinite" doesn't understand infinity.
Can anyone really embrace the entire concept of infinity? Why, that would take an infinite amount of time to totally understand every facet of infinity, wouldn't it? I do not claim to totally understand infinity, but I do have a view on it. It may be limited, but I still see it. Back to mathematics, take a ray. It goes on forever. Take the open end of that ray and move toward the starting point, stopping when you reach it. Will that journey take infinity? Yes. I agree with you on that point. Can a ray exist in reality? If you say yes, I challenge someone to make it. I personally say no, though.
4.) Anyone that thinks an infinite set of consecutive elements cannot be wholly traversed in a finite time does not understand infinity.
Start walking. If you reach an infinite point before you die, I'll believe you.
5.) Anyone that thinks the universe has "edges" or "boundaries" is invited to supply evidence for their existence. Surely there are some people in Stockholm that would be greatly interested in such a revolutionary observation.
I'm sure that the people at Stockholm are very interested in the subject of the 'expanding universe theory,' seeing as they were some of the people who proposed it. Please correct me if I'm wrong here, I do not like saying false things. I thought I made it quite sure that I explained it as a theory, not fact. If you took it that way, that is my fault. I will try to make that clearer.

Another thing I would like to make clear. This is all speculation, not the cold hard truth. I do not claim it is the truth. I only wish to pose a point and explain myself more if I am not understood correctly, in which case I will try to explain myself in a way that a person could understand. I may not succeed. I am not perfect. I leave perfection to God, who I believe is neither material nor mathematical. He is something else entirely, and I will not even try to explain Him. If anyone asks me to, I will ignore you.
 
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Eudaimonist said:
That's only "true" mathematically. It isn't clear that one can subdivide moments infinitely in reality.
Our very best observations indicate that space-time is continuous.


I'd love to hear an explanation of how this is possible.
Resolution of Zeno's Paradox for the win!

I don't have the time for a proper response to 52 cards latest reply. Hopefully I can get to it this evening.
 
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one love

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I think the misconception is in that people believe infinity has to apply towards the physical and philosophical world. It resides mathematically as an unbound set, with or without limits.

It definitely is NOT a number itself and this is where all misconception are start from. It is not a number, it is not a number on aplane or in a book, but rather it is a set.

It should be easy enough to understand infinity if you have taken high school algebra: e<x
 
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Another point I should make. Thank you Soul Searcher person. I should start up a talk about what reality is, unless there already is one or you want to take all the credit.
To respond to one love, I agree partially. It is quite true to say that it is a set, but if there are limits on the set of infinity, it totally destroys that set. Thank for bringing that up though. It was something I hadn't really thought about before.
 
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52Cards said:
Infinity cannot even begin to exist. This is due to the fact that if something starts, it has not existed forever in time, and therefore cannot be infinite.
Sure they can, they're called improper integrals.

There is no contradiction between adding up infinitely many terms and yielding a finite number; any line or space can be subdivided into infinitely many parts, where the addition of all of the individual pieces yields a finite length or area. You cannot even start to understand physics without calculus and infinities.

These kinds of infinities exist in reality. Perhaps you mean an infinite number of objects cannot exist in the universe, in which case you'd be right.
 
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If you keep dividing an line or space, when will it reach the point that you are dividing atoms? And after you divide the atoms, you divide the divide the subatomic particles. When will you reach the smallest object that can exist. Can it exist?

1/3+1/3+1/3=0.9999999999999999999999999 repeating
1/3+1/3+1/3=3/3=1
 
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NewToLife

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If you keep dividing an line or space, when will it reach the point that you are dividing atoms? And after you divide the atoms, you divide the divide the subatomic particles. When will you reach the smallest object that can exist. Can it exist?

The idea that the distance between 2 points can be divided infinitely is actually somewhat misleading, what it actually expresses is that you can keep on dividing the distance smaller and smaller so that you get a greater and greater number of points whose total approaches but never reaches infinity.
 
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MartinM

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52Cards said:
As we know now by the aid of scientific instruments, the universe is not infinite, but has boundaries that are constantly extending outwards, and have been since the birth of the universe.

No, no. That the Universe expands doesn't imply that it is finite - and even if it is, that doesn't imply a boundary.
 
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MartinM

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NewToLife said:
The idea that the distance between 2 points can be divided infinitely is actually somewhat misleading, what it actually expresses is that you can keep on dividing the distance smaller and smaller so that you get a greater and greater number of points whose total approaches but never reaches infinity.

Dividing the distance into smaller and smaller intervals doesn't give you any number of points; it gives you a finite number of line segments. The number of points in the interval is indeed infinite.
 
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NewToLife

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Dividing the distance into smaller and smaller intervals doesn't give you any number of points; it gives you a finite number of line segments. The number of points in the interval is indeed infinite.

From what I've seen what you are stating is not exactly uncontroversial, its a stretch to assert it as fact if you are speaking of reality, though it's fine if you are just speaking mathematically.
 
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