Inifinte integers between each interval of time

In summary: They're really the same problem. Imagine applying Zeno's paradox to the sweep seconds hand of an analog clock/watch: In five seconds the hand will move from one number to the next... But after 2.5 seconds it's only half-way there, and then it takes 1.25 seconds to cover half the remaining distance, and then .625 seconds to cover half the still-remaining distance... and because there are an infinite number of reals in between, there are an infinite number of steps to take, each one requiring some time. So how does the hand ever get there?
  • #1
Gurglas
3
0
Hey guys!
I am new here, and would like to ask a question that has been on my mind for a very long time. I've searched on the internet to find a solution to this question, but have come up with nothing, so I searched for a physics forum which could possibly put my question to rest.

Here it is:

Between each interval of time, there is an infinite amount of reals between them.

e.g. between 1s and 2s, (1.1s, 1.2s, 1.3s, 1.4s... 2s).
even between 1.1s, and 1.2s, (1.1s, 1.12s, 1.13s, 1.14s...1.2s)
even between 1.1s, and 1.11s (1.101s, 1.102s, 1.103s...1.1s)
and so on.

So technically between each interval of time, there has to also be an infinite amount of reals that will never be reached.

But then how can we ever even reach 2 seconds from 1 second?

How is it possible then that we perceive time as being constant, regardless of relativity.
 
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  • #2
1] The integers are 1,2,3,4... etc.
1.5 is not an integer
The number of integers between 1 and 2 is zero.

You mean the reals: 1, 1.1, 1.2, 1.3...2] Read up on Zeno's paradoxes. He had similar troubles. Look at Achilles and the tortoise. It was not resolved satisfactorily until more modern times.
 
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  • #3
DaveC426913 said:
1] The integers are 1,2,3,4... you mean the reals: 1, 1.1, 1.2, 1.3...
2] Read up on Zeno's paradox.

Sorry, I thought that was an integer :P lol

I've read about it, but that has to do with distances. How can we perceive time as constant if there are an infinite amount of "reals" between each interval?

thats my real question
 
  • #4
Gurglas said:
Sorry, I thought that was an integer :P lol

I've read about it, but that has to do with distances. How can we perceive time as constant if there are an infinite amount of "reals" between each interval?

thats my real question

Also read up on convergent series.

An infinite set of numbers can add up to a finite number.

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1

If you look at these number as fractions of a second, you can see how an infinite number of fractions of a second can pass in a finite amount of time.
 
  • #5
DaveC426913 said:
Also read up on convergent series.

An infinite set of numbers can add up to a finite number.

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1

If you look at these number as fractions of a second, you can see how an infinite number of fractions of a second can pass in a finite amount of time.

Thanks, unfortunately my calculus is limited to just second year uni, so it's a bit over my head :(
 
  • #6
Gurglas said:
I've read about it, but that has to do with distances. How can we perceive time as constant if there are an infinite amount of "reals" between each interval?

They're really the same problem. Imagine applying Zeno's paradox to the sweep seconds hand of an analog clock/watch: In five seconds the hand will move from one number to the next... But after 2.5 seconds it's only half-way there, and then it takes 1.25 seconds to cover half the remaining distance, and then .625 seconds to cover half the still-remaining distance... and because there are an infinite number of reals in between, there are an infinite number of steps to take, each one requiring some time. So how does the hand ever get there?
 
  • #7
Gurglas said:
Thanks, unfortunately my calculus is limited to just second year uni, so it's a bit over my head :(

It's over my head too. :smile:

Unless you're looking for rigorous proofs, don't worry about the calculus. Just look at the concepts.
 

1. What are infinite integers between each interval of time?

The concept of infinite integers between each interval of time refers to the idea that there are an infinite number of whole numbers or integers between any two points in time. This means that no matter how small the interval of time, there will always be more numbers within that time period.

2. How is this concept relevant to science?

This concept is relevant to science because it helps us understand the nature of time and the infinite possibilities that exist within it. It also has practical applications in fields such as mathematics, physics, and computer science.

3. Can you give an example of infinite integers between each interval of time?

One example that illustrates this concept is the time interval between two seconds. Even though this may seem like a small amount of time, there are an infinite number of integers between the two seconds, such as 1.5 seconds, 1.75 seconds, 1.9999 seconds, and so on.

4. How does this concept relate to the concept of infinity?

The concept of infinite integers between each interval of time is directly related to the concept of infinity. It shows that even within the smallest units of time, there are an infinite number of possibilities and numbers, highlighting the endless nature of infinity.

5. Are there any practical applications of this concept?

Yes, there are many practical applications of this concept in various fields. For example, in computer science, this concept is used in algorithms and data structures to optimize efficiency and accuracy. In physics, it helps us understand the nature of time and the universe. In mathematics, it has applications in number theory and calculus.

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