But, try and count the irrational or real numbers. Basically, I can do this no matter what crazy scheme you count with. Thank you, thank you, thank you. I do not exclude Cantor!!! There are no infinities larger than any other, because no matter what 'sophist Comparisons and distinctions of quantity or magnitudes cannot be made of 'things' concepts or otherwise that are NOT quantities or magnitudes!
Every type of 'infinity', by definition, goes on forever, it never concludes. Demonstrating that a counting system can be set up for some and not for others says nothing about the magnitude, or relative magnitude of either. Each goes on forever regardless of whether we can conceive one-for-one relationships between or among them.
So how does it "act like a number"? Additional comment: I don't care what kind of infinity or infinite set you may define, I can count them one-for-one as you produce another number from it.
So what's so deep about showing gaps in any proposed ordered counting system? Infinity is not a number. Any infinity can be counted by the natural numbers forever. It's smoke and mirrors to say any infinite set is larger than another assuming, without accepting, that the term 'infinite set' actually has any meaning.
Can a "set" be an unbounded amount? Possibly only in fantasy, which is what most discussion of infinities amounts to. The set of all the natural numbers exists, and therefore, the size of the set also exists. That size happens to be a non-finite number called Aleph-Null.
Your argument is wrong. And it does behave like a number because you can do basic arithmetic with it. In regards to time, surely 'infinity' is practically impossible. Since the concept of something neverending means that the number is always unattainable. It continues, infinitely, throughout time, but never can it BE infinite. At no point in time is something ever 'of infinite value'.
But presently, it continues. And it continues. And it continues, always. Therefore, the only possible infinity able to be 'of infinite value' is one that exists outside time? I can fully agree with the view that infinity is essentially the lack of boundary. However, the conclusion drawn from this in the previous post is nothing but a pseudo-philosophical game of words.
Here is an even worse example: "existence is the non-existence of non-existence". You get nowhere with this. If one looks carefully at the mathematical practice of set theory, it may be noticed that the members of a sets are rarely "being collected"; only very small finite sets arise like this. Instead, one considers a defining property of the elements to be collected.
When presented a potential element, one can in principle decide whether it satisfies the property or not. In programming, this is called "lazy construction". As all mathematical thinking is evidently finite, one will never face "actual infinity", but just finite formulations of properties. In regard of Cantor's result, there are more subsets of the natural numbers than one can formulate properties.
So there must be subsets without a defining property. Not surprisingly, little can be said about them except that they must be infinite.
They are like most of the transcendental numbers: vague generic objects filling the container. It should not be surprising that hard questions may arise with such objects, like the existence of sets with cardinalities in between countable and continuum. Infinity is no more a set than 'nothing'.
A set is defined. Nothing and infinity are not. Describe for me something that neither has nor lacks quality, quantity or location. Like infinity, nothing is the absence of a set. The fallacy is yours, not of the poster you're responding to. Naming it does not make it 'something' - it is only a name which refers to the absence of something. Something that is, by its very definition, a non-existence, cannot 'exist' in any physical or logical sense. No, actually, shadow is the wrong term.
The correct word is darkness. Darkness is non-existence of light. If non-existence existed, it wouldn't be a non-existence. Non-existence of black spots exists in a completely white paper. Non-existence of protons exists in electrons. They are just concepts. Just substitute exist with a different verb, e. One article has the definitive answer to the question 'does infinity exist? This website takes a common sense approach, and so people who like the weird things made possible by a belief in infinity will be sorely disappointed.
Infinity isn't something we can hope to understand yet. How can you add one to a number and it be the same? It follows none of the rules of normal numbers. If you add up all the integers and fractions before it you will get 0.
We can't solve the problem of infinity because it CAN'T exist. Amount of space, amount of paper, amount of particles in the universe! If there is always a limiting factor, then nothing can be endless. So infinity is a game, not a possibility.
Unfortunately, humanity humans will never know, or be able to fully understand infinity, or if it exists. Hypothetically, if you were able to prove that infinity does exist, then would that not make you God? I am not a religious person, but the answer to infinity lies with our creator. My understanding is that the universe is always expanding and is therefore Infinite. But if we had the tools and we could break the speed of light could we measure the different stages of infinity?
The explanation that the universe started with a big bang then expanded and suddenly expanded by infinity does not make too much sense to me. We are able to measure a less than 1 millisecond after the big bang. That is still something and a number that we can measure from the stages to infinity isn't it? I feel as this article is trying to discredit some of the great theologians such as Gottfried Wilhelm Leibniz who attempted to use reason to prove the need for a being to begin the universe an unseasoned reasoner.
Let me explain why these philosophers are right about the non-existence of infinities. The most basic of these arguments was made by the Christian philosophers and perfected by Muslim philosophers and was called the Kalam argument. It attempts to prove that the universe had a beginning and is not infinite. So, first, what is an infinity? An infinity is a limitless quantity, in other words, an infinity, by definition, cannot be quantified.
The kalam argument looks at two types of infinities: potential and actual. A potential infinity is like a stop watch, if you hit start it could, potentially, continue adding numbers onto each other for a limitless amount of time.
The other type of infinity, an actual infinity, is an unquantifiable amount of something, something that cannot be calculated because it goes on and on forever. The argument then proves that time had to have a beginning and is not infinite. If now exists time cannot be infinite. Ok, picture "now" as a destination on a set of train tracks. How far would you have to travel to reach your destination? There is no point of reference in an infinity because it is unquantifiable.
Ok, so time isn't infinite, so what? So then why does the universe exist, did it one day in its nonexistence decide to pop into existence. This is impossible because A the universe is not personal and cannot decide B something that does not exist cannot reason itself into existence. This brings us to the conclusion that there is something that is immaterial, personal, self existent, "outside" of time, and logically necessary that started the universe.
You do realise that you're wrong on several accounts and that Kalam argument doesn't work, right? I will criticise a couple of points briefly. Firstly, if time of universe's existence is finite 'time' is not a proper word here, which you seem to have ignored then there's no reason that there has to be a point that nothing existed.
Also, requiring that "logically necessary" thing to "exist 'outside' of time", be "immaterial", "personal", "self existent" because "universe can't decide to reason itself into existence" is jumping to conclusions. Also, are computers "personal" as in, what you mean by the word "personal"?
Because they somehow can vary their output depending on the input. Also, the Kalam argument is irrelevant to the topic. Firstly, the Kalam cosmological argument doesn't state that there must be a point at which nothing existed, it simply states that there was a time before which there was no time or space, or matter, or anything else actually.
And this is supported by the majority of astrophysicists and other scientists. Secondly, the idea of a timeless, spaceless, immaterial, incredibly powerful Being who has aseity does not jump to any conclusions.
It can be deduced from the properties that must be assigned to whatever caused the universe, whether that was God or not. The only alternative to that would be that an abstract object caused the universe to exist, but that simply makes no sense because abstract objects simply have no causal properties.
The one thing that no proponent of the KCA has ever provided is the cause of the first event. Now you might reply - this was the First Causer aka the Personal Creator or whatever name you want to use. But this refers to the causer not the cause. So you need to identify what the First Causer did first. The problem that you face is that the First Causer exists unchanging.
And to do something requires change. But this is impossible for something that is unchanging. But then you can re-define some words to provide a way out of this, just as other proponents have done Infinity is the non-existence of a limit. If a non-existence existed, it wouldn't be a non-existence.
The nonexistence of a limit could also just mean that space,time, light, and matter are constantly being created everywhere not that nothing exists but if you want to get philosophical with it go ahead.
Nothing is still a thing. The article states that infinities in Quantum Electrodynamics is viewed as renormalization problems. However, it is my understanding of Quantum Field Theory QFT that infinities are not just a matter of a renormalization problem but a necessary property of the condensate - otherwise the theory would not work at all. Thank you for this page. I am sick of hearing about how there are an infinite number of worlds so there is one just like this one Infinity is an old human concept, usefully employed in mathematics as 'shorthand' for very huge.
But it isn't a 'thing' - it can never 'be' because you never get there. If the mass at the centre of a Black Hole was infinite why don't they just swallow up the whole universe like a huge reverse-big-bang vacuum cleaner, why have a horizon at all if you're 'infinite'? The nonsense theories appear to be due to the paradoxes caused by trying to take this 'concept' literally. What interests me most about the possible existence of physical infinites is their ability to predict an infinite number of universes under the multiverse theory If space is indeed continuous, there could be infinite possible positions in which something could be in exactly the same way as there are infinite numbers between 0 and 1 and for a probabilistic event, such as the position of a quantum particle, an infinite number of universes would be required again, assuming its truth to describe the position in spacetime of that particle alone.
Skip to main content. Does infinity exist? The even numbers are in one-to-one correspondence with the natural numbers. Simulated view of a black hole.
Image: Alain Riazuelo. There is also an infinite number of rational numbers between any two irrational numbers. That's not correct Permalink Submitted by Anonymous on July 27, For example, if you picked these two irrationals: 3. Just truncate the larger number after the first digit where it differs from the smaller number: 3. If you prefer rationals written as fractions, then just write it over a power of ten: And that fraction is guaranteed to be between the two irrationals.
I'm confused about this. Motion implies velocity, distance and time, not just distance Permalink Submitted by Anonymous on September 16, Zeno's paradox Permalink Submitted by Anonymous on March 17, So is infinity a mathematical construct, or does it really exist?
Im curious what conclusions other people might draw. Zeno's paradox Permalink Submitted by Anonymous on December 31, But the video game analogy Permalink Submitted by Enai on August 28, No Permalink Submitted by Patrick on February 18, Support that infinity exists and the universe is inside of it Permalink Submitted by Ron C on January 21, Since it is part of infinity there is no particular identification for that specific potential Imagine the universe is a drop of water in the ocean.
Zenos paradox is nothing but semantics. Permalink Submitted by Q on June 13, Countable vs. Permalink Submitted by Anonymous on June 4, Not a number says who? Infinity is not a real number.
In terms of solutions of limits, it means that the equation you are taking the limit of will go in that direction forever. For example:. You can imagine it going off the page and continuing upwards. In other words, the limit as x approaches zero of g x is infinity, because it keeps going up without stopping. Likewise if you had:. The limit as x approaches zero would be negative infinity, since the graph goes down forever as you approach zero from either side:.
As a general rule , when you are taking a limit and the denominator equals zero, the limit will go to infinity or negative infinity depending on the sign of the function. So when would you put that a limit does not exist? When the one sided limits do not equal each other. First, a one sided limit is when you approach a value from a single side.
And, things are not the way they are not. This is true for literally everything in existence. Now re-examine the concept of infinity.
More than A. Think about it: if a thing is not more than itself, it is complete, and therefore finite. Thus, it becomes clear why infinite circles do not exist. The concept is logically contradictory. The same is true for infinite sets, infinite magnitudes, infinite distances, or anything else. If a set is a set, then it is itself and no more. If a magnitude is a magnitude, then it is itself and no more. If a circle is a circle, then it is only itself and nothing more. There is no circle which you can conceive of which I cannot double in size.
There is no inherent limitation to the size of circle we can imagine. Infinity must strictly be understood as shorthand. It is never an adjective for a concrete noun. Consider one more example to illustrate the difference between an incoherent definition of infinity and a coherent one. But not just any rubber band — and extraordinary one.
It will stretch as far as you stretch it. This irrational interpretation is how mathematicians conceive of infinite sets. They are extreme.
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