How true is the statement from John Green's book that "some infinities are greater than other infinities"? Is it possible to compare something that has no end?

First, you need to understand the meaning of the word “compare” -oddly enough, people understand it differently. 1)Some people think that “compare” means comparing, hoping that some – or all – of the parameters of the entities being compared that are accessible to perception and awareness will be the same. This is the “what if…?” approach. 2)Another way to understand it is to assume that you can work with entities of ANY nature according to the SAME rules and see what happens. This is the “where do you go from a submarine?” approach. It is fraught with, or rather almost always guarantees, the occurrence of so-called paradoxes or aporias. The reason for their occurrence is that in the course of reasoning (or before it, setting the conditions for consideration), that is, attempts to explain what is observed or discussed and their position on this issue, participants intentionally or unintentionally substitute a QUALITATIVE characteristic for a QUANTITATIVE one (or vice versa), or if the system is not static, but time is entered – while the quantitative characteristic becomes a process, and the qualitative So – neither compare, i.e. point 1), nor work according to the SAME rules, i.e. point 2). 2) with entities of DIFFERENT-quantitative and qualitative nature (and their derivatives-process and state) NE-L-ZYA! This is a gross methodological error! Unfortunately, some, even great scientists, sages, so to speak, both in ancient and modern times, do not understand this difference, well, approximately, as colorblind people due to visual defects do not distinguish certain colors. For example, Zeno's aporia would not have appeared if he had understood the difference between a process and a state. He believed that movement is both a process and a state, but it cannot be so. If we think of movement as a process, we get one picture of the world around us; if we think of movement as a state, we get a completely different picture of the world. This is the reason why Einstein's Theory of Relativity and quantum mechanics cannot be combined. Einstein's theory, being a special case of Noether's theorem, assumes that space is almost everywhere continuous, and the number of discontinuity points (for example, black holes) is no more than countable. Quantum mechanics, on the other hand, considers space to be discontinuous almost everywhere, and the number of regions of continuity ( and the radius of these regions is an infinitesimal value) is no more than countable. When working with mathematical “infinities”, one should have a good idea of their nature, what physical features of the surrounding world they are a reflection of…

Yes, it is. For example, the simplest infinity is the infinity of a natural number series: 1,2,3, etc. But the infinity of real numbers, that is, for example, points on a segment, is a much more powerful infinite set. Such points cannot be counted or numbered. All this is studied in higher mathematics.

There is a version that the universe is expanding not in one continuous spot, but in an infinitely growing number of such spots. That is, if you spray the brush on the canvas, a few small spots will appear. Now imagine that the number of these small spots tends to infinity. Each of them also grows or shrinks in diameter indefinitely. So, yes, the probability that the rate of expansion of one of the spots is greater or less than the other is obvious. But this does not mean that there is no longer infinity as such. More of its tendency to expand.

Here are a lot of natural numbers – there are a lot of them.

There are also a lot of even numbers, but exactly as many as odd ones.

There are also many fractions of the form m/n (the numbers m and n are natural), but exactly the same number as all natural numbers. Even if there are exactly the same number of points on a line segment as on the entire line, but more than all fractions, even though all sets are infinite.

I have heated arguments with mathematicians on this very topic. That's what I came up with. For mathematics, the main thing is to measure and enter the ratio between everything that is possible. For philosophy, the main thing is to define the idea of everything that can be done. Since infinity cannot be accurately measured, but only its idea can be determined, then mathematics does not work here. Here the disadvantages of the mathematical method of cognition are revealed. In philosophy, infinity can be represented as an idea or phenomenon.

I think it's really absurd to compare something that doesn't have an end. Let me clarify – to compare, precisely by introducing clear relationships with other things, since, when talking about anything, we will never get away from comparisons.

Even if we assume that there are many infinities, we can only compare them by their known parts (intervals). For example, it is completely absurd to measure something that does not exist yet, which will only appear in the future. And infinity is a thing that will never end in the future.

Hence, my definition: infinity can be represented as an incomplete process that will continue forever.

If we are talking about infinities with similar parameters, then we can compare them, but not in terms of what is infinite in them. If we are still talking about properties that relate specifically to the infinity of very similar objects, then we can compare individual segments, but not the entire infinity, since we are not able to understand it. The very concept of infinity is rather vague – I think everything can be measured. However, if we are inside a certain space that we cannot realize (or see from the outside), then by our standards it will seem infinite.

PS if the question is about “infinite” people, then yes, they can be compared in so many ways: D

First, you need to understand the meaning of the word “compare” -oddly enough, people understand it differently. 1)Some people think that “compare” means comparing, hoping that some – or all – of the parameters of the entities being compared that are accessible to perception and awareness will be the same. This is the “what if…?” approach. 2)Another way to understand it is to assume that you can work with entities of ANY nature according to the SAME rules and see what happens. This is the “where do you go from a submarine?” approach. It is fraught with, or rather almost always guarantees, the occurrence of so-called paradoxes or aporias. The reason for their occurrence is that in the course of reasoning (or before it, setting the conditions for consideration), that is, attempts to explain what is observed or discussed and their position on this issue, participants intentionally or unintentionally substitute a QUALITATIVE characteristic for a QUANTITATIVE one (or vice versa), or if the system is not static, but time is entered – while the quantitative characteristic becomes a process, and the qualitative So – neither compare, i.e. point 1), nor work according to the SAME rules, i.e. point 2). 2) with entities of DIFFERENT-quantitative and qualitative nature (and their derivatives-process and state) NE-L-ZYA! This is a gross methodological error! Unfortunately, some, even great scientists, sages, so to speak, both in ancient and modern times, do not understand this difference, well, approximately, as colorblind people due to visual defects do not distinguish certain colors. For example, Zeno's aporia would not have appeared if he had understood the difference between a process and a state. He believed that movement is both a process and a state, but it cannot be so. If we think of movement as a process, we get one picture of the world around us; if we think of movement as a state, we get a completely different picture of the world. This is the reason why Einstein's Theory of Relativity and quantum mechanics cannot be combined. Einstein's theory, being a special case of Noether's theorem, assumes that space is almost everywhere continuous, and the number of discontinuity points (for example, black holes) is no more than countable. Quantum mechanics, on the other hand, considers space to be discontinuous almost everywhere, and the number of regions of continuity ( and the radius of these regions is an infinitesimal value) is no more than countable. When working with mathematical “infinities”, one should have a good idea of their nature, what physical features of the surrounding world they are a reflection of…

Yes, it is. For example, the simplest infinity is the infinity of a natural number series: 1,2,3, etc. But the infinity of real numbers, that is, for example, points on a segment, is a much more powerful infinite set. Such points cannot be counted or numbered. All this is studied in higher mathematics.

There is a version that the universe is expanding not in one continuous spot, but in an infinitely growing number of such spots. That is, if you spray the brush on the canvas, a few small spots will appear. Now imagine that the number of these small spots tends to infinity. Each of them also grows or shrinks in diameter indefinitely. So, yes, the probability that the rate of expansion of one of the spots is greater or less than the other is obvious. But this does not mean that there is no longer infinity as such. More of its tendency to expand.

Here are a lot of natural numbers – there are a lot of them.

There are also a lot of even numbers, but exactly as many as odd ones.

There are also many fractions of the form m/n (the numbers m and n are natural), but exactly the same number as all natural numbers. Even if there are exactly the same number of points on a line segment as on the entire line, but more than all fractions, even though all sets are infinite.

Isn't it amazing?

I have heated arguments with mathematicians on this very topic. That's what I came up with. For mathematics, the main thing is to measure and enter the ratio between everything that is possible. For philosophy, the main thing is to define the idea of everything that can be done. Since infinity cannot be accurately measured, but only its idea can be determined, then mathematics does not work here. Here the disadvantages of the mathematical method of cognition are revealed. In philosophy, infinity can be represented as an idea or phenomenon.

I think it's really absurd to compare something that doesn't have an end. Let me clarify – to compare, precisely by introducing clear relationships with other things, since, when talking about anything, we will never get away from comparisons.

Even if we assume that there are many infinities, we can only compare them by their known parts (intervals). For example, it is completely absurd to measure something that does not exist yet, which will only appear in the future. And infinity is a thing that will never end in the future.

Hence, my definition: infinity can be represented as an incomplete process that will continue forever.

If we are talking about infinities with similar parameters, then we can compare them, but not in terms of what is infinite in them. If we are still talking about properties that relate specifically to the infinity of very similar objects, then we can compare individual segments, but not the entire infinity, since we are not able to understand it. The very concept of infinity is rather vague – I think everything can be measured. However, if we are inside a certain space that we cannot realize (or see from the outside), then by our standards it will seem infinite.

PS if the question is about “infinite” people, then yes, they can be compared in so many ways: D