 1. vadim_romansky says:

The question, in my opinion (maybe I'm wrong) is not put correctly. Infinity is not a mathematical category, but a philosophical one. Together with the category” finite”, it forms a pair similar to the pairs of other categories: left and right… Mathematical infinity is a particular manifestation of the category of infinity in the world of numbers, numbers, functions, geometric figures, etc.Infinity does not exist by itself (as “right”, without “left”), it only reflects its opposite – the category of “finite” (that which has a beginning and end in time,space,etc.). Mathematical infinity should be distinguished from the concept of “infinity” (for example, a circle or ball; they are limited in space (length, area), but do not have a definite beginning and end). There is also a distinction between “potential infinity “and”actual infinity”. The category of ” potential infinity “is perceived by the mind – it is simply the POSSIBILITY of realizing a certain phenomenon, object, etc.an” unlimited ” number of times (under the appropriate conditions). Although even here there is a problem: the number of” implementations “is limited by the” shelf life “of the conditional” mechanism ” (a person can wash a lot of dirty dishes until he falls down exhausted).

The category of “actual infinity” is the main difficulty for the human mind to perceive and comprehend. We cannot yet understand this category, we cannot “visually represent”it.Although there is one example: two mirrors placed strictly parallel to each other, in fact, give us the image of” actual infinity “(when the reflection of the mirror format” shrinks ” to a point).

But! At the level of logic, it is not yet possible to understand actual infinity – this leads to ANTINOMIES (conclusions that contradict each other) An example is known: if the universe had a beginning in time, then the question arises: what then was before the BEGINNING of the Universe? (was there a time when there was no time?). On the other hand, if we assume an infinite time of existence of the Universe (they say, it has always been), then we come to another incomprehensible conclusion: so we who live today, “here and now”, close an INFINITE SERIES of time that has passed before us? So be it,but how do you UNDERSTAND it?

CONCLUSION: so far we are not able to understand the category of “actual” Infinity. Most likely, we do not have enough knowledge about other philosophical categories – they are very difficult to understand and “isolate” (the situation with categories resembles the “periodic table” in the time of Mendeleev himself- “half” of the elements of the “periodic table” was simply not known to chemists).

Mathematicians, apparently, did not particularly bother to think about the essence of philosophical categories (the attitude to philosophy as a science among “subject specialists” has always been arrogant). Perhaps this is the reason (I may be wrong) that G. Cantor's “Theory of Infinite Sets” found problems.

In the meantime… Apparently, the question posed in the title: “Can one infinity be greater than another?” has as little meaning as the question: “Can one left boot be more left than the second?”

2. evgeny_kashtanov says:

Can. For example, natural numbers are infinitely many and real numbers are infinitely many, but there are more real numbers. This means that if we try to match every real number with a natural number, then we will not succeed, no matter how we do it, i.e., in other words, all the natural numbers will not be enough for all the real numbers. To estimate the cardinality (i.e., quantify) of infinite sets, we came up with the so-called cardinal numbers. Each of these numbers corresponds to its own infinity, and each infinity is greater than the previous one. These numbers are denoted by the Hebrew letter ℵ (aleph). The cardinality of a set of natural numbers or the cardinality of a countable set is the smallest of all possible infinities. It is denoted by ℵ0, the cardinality of the set of real numbers is denoted by the letter ℵ1, and so on. Each subsequent infinity is obtained as the cardinality of the set of all subsets of the set of the previous cardinality. I.e., ℵ1 is the cardinality of the set of all subsets of a countable set. ℵ2 is the cardinality of the set of all subsets of the set of cardinality ℵ1 (also called a continuum), and so on.

3. andrey_perepelkin says:

If you ask yourself this question and start exploring one and the other infinities, you will eventually come to the place where they connect! And all this together turns out to be one infinity.

It's like you can talk about abstruse things endlessly, and in the end you will come to the conclusion that infinitely many people have done this before you.

And that you're not the only one who did it and who will continue to do it.

And you are all part of the same infinity.

And when you come to such conclusions , you will feel so good in your heart, so pleasant that you will even calm down and want to go for a cup of tea, dreamily looking at the moonlit sky, where you can't see the stars.

4. viktor_palych_shestipalov says:

Yes, but this is best described by Michael on the Vsauce channel. You can watch the video in translation, it is called ” How to calculate beyond infinity? (Vsauce in Russian)”

5. alexey_kuznetsov says:

The question is not correct. More or less is for comparing numbers, and other concepts that have a digital dimension. Infinities can be compared in power, but not in size. This is an analog of how to ask: what's bigger? Red or green? Or which is sweeter than 5 or 13? How much will it be if you add up three pencils and the current strength.

6. yuri_tablin says:

Absurd! How can infinity be greater than itself? If we say that something is greater than something, then we are talking about two finite phenomena “something” and “something” that can be measured, while measuring infinity – something eternal and absolute-is absurd, because no matter how much we measure, we would inevitably limit, and what is measured would become finite, But then we should say that infinity is greater than finite, and not as in the title. If you will, this is God-eternal, invisible, unknowable, unborn and uncreated, who is always greater than all that exists. And there are no two Gods (two absolutes), because God is one in himself!

7. sergei says:

If there were at least one infinitely large body in the universe, then there could be no place for other bodies in principle.

If there were even one infinitely long straight line, there would be no place in the universe to place it.

If “mathematics” allows manipulation of concepts that obviously do not have a material identity, this is not mathematics.

If the mind accepts such assumptions …

Then it's just the mind.

Weak man, chozha. And greedy.

It is quite another matter if a person has made a miracle melenka. Which spits out infinitesimal pies for an infinitely long time. But a lot.

That yes. So it happens in real life. And the endlessly chewing person constantly devours them. While remaining endlessly hungry.

And where to put them patamushta?

8. evgeny_lepeshev says:

Infinity is a relative quantity and basically means a process? Take two hoops:20 centimeters and 80 centimeters in diameter.Determine the starting point on each hoop, and from that point, start plotting the length of the hoop. This process is infinite in time. Do you think the data is equal to infinity? With respect to the process, they are equal! And in relation to the hoop-the final value is comparable!

9. boris_sergeyevich_kashirsky says:

Of course it can. Let's assume that by size we mean the length of a segment. Then the open segment (gap) with a length of 2 cm is larger than the open segment with a length of 1 cm. Moreover, both of them are infinite, i.e. they have no end

10. nickvg says:

No. Infinity is something that cannot be measured. And everything that is measured has a beginning and an end, and therefore is not infinite. If something is greater than something, then it is no longer infinity.

11. dmitry_gor says:

Of course it can! In numerical terms. Let's say that in a universe with infinite mass, its mass in grams will be less than its mass in ounces. Both numbers are infinite, but in one case the numerical expression creates an inequality a priori.

12. victoria_klyagincheva says:

He can, but he doesn't want to. If he wants to, he can do it. Because anything can happen indefinitely. Even what no one else can do. And even more so will be able to do what he wants. It remains only to understand which of them will do it first.

13. digital_joint says:

First, you need to understand the terminology. Infinity is not eternity, if anything. Forever it is continuous and does not repeat itself, and the term “infinity” is often applied to events that are looped on repetitions. For example: “endlessly walked around the room from wall to wall”, and if “forever walked around the room from wall to wall” already sounds like some kind of nonsense. Further. If we proceed from this logic, it means that eternity is linear, continuous, without beginning or end, vast, encompassing, incomprehensible. And it is indivisible and unique. It cannot be compared to another eternity, there is no other eternity. Forever alone. And infinity can be spiral, that is, segmented, increasing in duration, or cone-shaped, when each subsequent turn is larger than the previous one. A friend from the mathematical comment about something like this through functions and logarithms and tried to explain. I.e. they have infinity, it is discrete, consisting of a certain set of numbers, and therefore, if these numbers in one case and according to the same rules grow slower by some unit of time, then other numbers, by the same unit of time, but with different rules grow faster, and therefore the second infinite sequence of numbers seems to be larger. Although in fact, you asked about something else: how to evaluate one continuous something, through another continuous something. But this very continuity or permanence, or constancy, is the antipode, the antonym of discreteness-discontinuity. That is, infinity is like ripples in the eyes, like the lambs of waves on the ocean canvas that you look at standing on the shore and that break on the cliff under your feet. And eternity is like a still lake without a beginning and edges, when you are in its center and there are no reference points, there is no edge and you do not understand how you got here and what they eat with it. I.e. infinity has at least a reference point from the edge, but eternity does not – look around, but everywhere the same thing. Therefore, eternity cannot be compared with another eternity, the lake is one. And infinity, probably yes, there are a lot of waves with foam lambs.

14. denis_bulldozer_elistratov says:

When we say that a certain quantity is potentially infinite, we mean that it can be indefinitely increased. An alternative is the concept of actual infinity, which means that it is considered (as a really existing) quantity that does not have a finite measure. Example: Euclid's second postulate does not state that the length of a straight line is infinite, but simply that “a straight line can be continuously extended”. This is a potential infinity. If we consider the entire infinite line, it gives an example of actual infinity.

15. walter_kraft says:

Of course it can. After all, Allah is stronger than Christ and Yahweh. Actually, it's a lot of nonsense. Infinity means that no matter what number we take, there is always another even larger number.