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infinite small or large, infinite slow or fast, infinite long time or short, any kind of infinite counts. Are there any real-life example out of Math, that is infinite?

This is the whole knowledge I know now:

size: I know Planck length is the observation size limit, so, are there 0 point particles exist?

Electrons don't have size, but is it the same to say "don't have size " and "size is 0"?

Observable universe have a 45 Billion light year radius, so there is a maximum size limit, right?

time: Planck time is the shortest time; the life span of the universe is the longest time.

speed: Light speed is the fast limit; 0 kelvin does not exist, so 0 speed does not exist.

mass: The energy of our universe is finite so the mass is finite, information is finite too.

difference: not only 0 speed does not exist. all rational number are not exist, all number are not constant, in real life. Can you find exactly 3 apples? no matter how did you define what is "a apple" you always get more or less amount of your definition in real world.

Did I made mistakes? Are there any examples that are infinite?

P.S. I don't know which tag this question belongs to. help me to add them please.
P.S. help to Solve the question, not Block the question, please.

WonderWilson
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  • No one has come up with an experiment to determine whether or not there is an infinite amount of something, and perhaps such an experiment is impossible. I don’t see how a measurement detector/interpreter could distinguish between a Graham’s number of something and an infinite number of something. Also, I don’t see the utility of such an experiment. – Adam Rubinson Feb 22 '21 at 14:04
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    This question may have been asked already. Is this what you are looking for: https://physics.stackexchange.com/q/290445/276737 – Cream Feb 22 '21 at 14:18
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    Does this answer your question? Has infinity been observed yet? – Cream Feb 22 '21 at 14:21
  • @Cream no, not really. the title was asking the same question, but "are there?" "No" didn't really answering the detail questions in my description. but thanks for helping. – WonderWilson Feb 22 '21 at 14:29
  • thanks, @Adam, yes, I think proving infinite is a problem, now. I changed the question, included "possible infinite". but I heard they have a test about our universe's space curvature, that's 0. they said it maybe means our observable universe is a very small part of the whole universe, I don't know the detail. but they do have some method to prove infinite, maybe. – WonderWilson Feb 22 '21 at 14:38
  • "Two Things Are Infinite: the Universe and Human Stupidity; and I'm not sure about the Universe", attributed (with some controversy) to Einstein. See this discussion: https://skeptics.stackexchange.com/q/18140/45073 – ZeroTheHero Feb 22 '21 at 14:42
  • Thanks @ZeroTheHero, I don't think it's a clever sentence from a such great man. "Infinite stupid" based on "knowledge is infinite", based on "information in our Observable Universe is infinite". that is not true. – WonderWilson Feb 22 '21 at 14:48
  • You say “outside of math” but there are plenty of instances in math that relate to physically realizable systems. Probability has lots of examples. There are events which are possible, but with probabilities that decrease with time quickly enough that the expectation value of the length of time you’ll have to wait for the event to happen is infinite. That is an infinite time interval which is an attribute of a real physical system. – Ben51 Feb 22 '21 at 15:39
  • Thank you @Ben51 , "we need a number" does not mean the number exist in real world. we need infinite time, does not mean there is infinite time. universe have a life span. – WonderWilson Feb 22 '21 at 15:56
  • If it helps: There is no number in the integers, or in the real number system called "infinity." There are infinities in some specialized branches of mathematics, but those are not used to quantify any physical things. The closest we come is in calculus where we can talk about how one quantity approaches some limit while some other quantity increases without bound or vice versa. Sometimes, we say "goes to infinity" as a synonym for "increases without bound," but that's somewhat of a colloquialism, rather than strictly formal math. – Solomon Slow Feb 22 '21 at 15:56
  • some people just try his best not to solve the question, but to Block the question, redirect it to no answer land. good job for no help. Thank you guys, who give any ideas to this question. sorry to those guys who want to give more but can't, because the question is closed. – WonderWilson Feb 22 '21 at 16:04

3 Answers3

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Answering your question depends on our models. In classical physics, we can talk about zero velocity. If you don't count it, as its not quantum and relativistic, then we can ask whether QM and GR are fundamentally true to all orders of magnitude. They don't seem to be. So would any example count?

Some other examples could be:

  • The zero mass of the photon (to our best experimental knowledge)

  • The zero difference between the speeds of light and gravitational waves

  • The infinite ratio between the mass of the electron and the mass of the photon

  • We can, in fact, take the inverse of any observable with value zero, and get an infinite observable.

Rd Basha
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  • thank you Rd Basha. I think 0 velocity just exist in model, which is in pure math. the same are 1m/s 2m/s speed, 3 or 4 apples, there always more or less, not never exactly 3 apples. there is no rational number in real world. so I think light speed is the same. they are all big-scale world, roughly non-constant in detail number. – WonderWilson Feb 22 '21 at 15:00
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Our senses can't sense something infinite, or a infinitesimal difference. Similarly with any instruments we use to measure things.

Our theories and mathematics may work out more smoothly if we assume such things are possible.

So for example, one way to measure waves is in cycles per second. Imagine you have a use for the inverse measure, seconds per cycle. Then the slower something cycles the bigger the number, and something that has no cycle would have an infinite measure.

Is it more convenient to be able to record the absence of a cycle as an infinite value, or to not be able to?

It isn't about reality, it's just about how we want to organize our thinking.

J Thomas
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  • Thank you. yes, as in the question comments @Adam Rubinson said, experiment accuracy is a problem to directly prove infinite. so I changed the question, included "possible infinite".if we don't know the limit, then the example counts as possible infinite. in your example, the detector is designed to have a low accuracy when the wave length is longer. so it is not a good example of "we don't know the limit". – WonderWilson Feb 22 '21 at 15:44
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IMHO, it's a very hard question. At first, everything is a concept in our head, because we process outer world information given by our sensory organs (eyes, ears, etc.) and filtered / reconstructed by our brains. What we actually perceive is a "brain model" of the world, not the world itself. Some concepts can be "harder" than others, such as $0$ or $\infty$. One can argue that zero is more realistic than infinity, but I do not agree on that. At last, they are closely related : $\boxed {\infty = \lim_{x\to 0} 1/x}$ and $\boxed {0=\lim_{x\to \infty}1/x}$.

Another interesting fact is that we can arrive to indeterminate forms, manipulating with zero or infinity alone or with them both in conjunction :

$$ {\frac {0}{0}},~{\frac {\infty }{\infty }},~0\times \infty ,~\infty -\infty ,~0^{0},~1^{\infty },\infty ^{0}. $$

The fact that indeterminate forms ties together zero and infinity also means something.

Can you prove to me that you really have zero apples ? Maybe you have one under your back or wherever you want it to hide ? Is it realistic, that you note that you don't have something ($0$ amount) ? You may have 0 apples, but 0 dragons as well. Finally if we agree that zero has some "realistic sense" then so does the infinity too. Because zero is what is left to you when you pass 1 apple to infinite amount of people for tasting it. Line is just an infinite amount of co-linear points. Circle - polygon with infinite amount of edges, etc. So in my opinion, either we have both notions $0,\infty$ in reality or none of them.

Agnius Vasiliauskas
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