RE: Actual Infinity in Reality?
March 3, 2018 at 1:26 pm
(This post was last modified: March 3, 2018 at 1:30 pm by RoadRunner79.)
(March 3, 2018 at 1:00 pm)polymath257 Wrote:
Quote:1. yes, between any two real numbers, there are infinitely many real numbers. I agree.
2. Let's be more precise. Yes, whenever you are *between* 0 and 1, say 0<x<1, there is another point y with x<y<1.
3. Let's be more precise. Whenever 0<x<1, there is a point y with 0<y<x.
4. I agree with both of those as I stated them.
OK, so where is the problem?
So as we progress from say 0 to 1, there is always another point Y between X and 1 where X<Y<1.
If you must pass through each of these points, you will never reach 1, because there is always another point Y which must be met.
Therefore Zeno concluded that if you can never end your journey or on the inverse (which isn't quite as intuitive) never begin your journey,
then motion is impossible. If you have to complete a endless number of points before you can get to the end (1) then you will never be at the end (1)
Do you agree? If not, where do you think that the error is?
(March 3, 2018 at 1:00 pm)polymath257 Wrote: On an integer line, there is no possible space between 1 and 2, or for that matter 2 and 3 to make a separate number. Are these equal as well?
No, the difference between them is 1, which is not zero. In the other example, the distance between is zero.
I would agree, if they are the same, then they are equal.... that there is no space between them could be confusing.
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. - Alexander Vilenkin
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther