# Inifinte integers between each interval of time

1. May 23, 2012

### Gurglas

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.

Last edited: May 23, 2012
2. May 23, 2012

### DaveC426913

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.

Last edited: May 23, 2012
3. May 23, 2012

### Gurglas

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. May 23, 2012

### DaveC426913

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. May 23, 2012

### Gurglas

Thanks, unfortunately my calculus is limited to just second year uni, so it's a bit over my head :(

6. May 23, 2012

### Staff: Mentor

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. May 23, 2012