
Originally Posted by
randynewman666

Originally Posted by
William McCormick

Originally Posted by
randynewman666

Originally Posted by
MagiMaster
One way to look at the 0.9999... question is to consider this: what is 1 - 0.9999...? The answer, 0. Therefore, yes, 0.9999... = 1. Actually, there are many, many ways to show that this is true, at least for the real numbers. There are number systems out there where it isn't true anymore, but those systems aren't what we're used to.
BTW, the real world doesn't seem to contain any true infinites. The universe is composed of finitely many particles of a finite size with a finite amount of energy existing within a finite amount of space over a finite amount of time. :/
arent there an infinite amount of points in any given space?
Yes, you can keep dividing a linear space, a one inch straight line, until no human could ever in his lifetime conclude one way or the other, if the divisions are actually there.
A human would not be able to count them or measure them in one lifetime or measure them by any human standard. But mathematically and realistically they could exist even if there was no way to verify them.
In other words when electrons move, I highly doubt they jump from the smallest grid or increment we can measure, to the next grid or increment we can measure. I would say they move along smoothly in infinitely small increments.
But the fact that we cannot see them. Means we assume that they don't jump from one place to another. They might move like Mexican jumping beans for all we know.
Sincerely,
William McCormick
The idea of being able to divide a space in reality infinitly has always boggled my mind. When electrons move I wouldnt think they jump from one finite place to another but how can they be described as moving smoothly along infinitely small increments? It would still be moving in increments. We try to describe infinity in math, which doesnt seem right to me. I think Infinity exists in nature but I think we just dont comprehend it yet.
I would think that electrons slow and positively accelerate as they move through matter. But their overall movement is probably a very smooth motion. I would say infinitely smooth.
I know where moving objects are caught on high speed film, or movie film, they show a jittering jerky movement. We often relate that to the actuality. The truth is that it is just the restricted speed of the recording device, that creates the jerky movements.
I would imagine if you tried to film an electron you would get that same jerky motion. However the reason would be the particles carrying the picture of the single electrons movement would come to the recording device intermittently and in different areas of the media.
Causing a guaranteed jerky picture. And loss of focus, as you wait for enough particles to hit the entire recording surface, and create a change in that surface, representative of the actuality.
To me this is all an amazing speculation though. Because I know they were here in the early 1900's and they all agreed that an electron will never be seen. And they were mighty crafty back then.
If you tried to film an electron, you would have to wait till the electrons that bring you a picture get to the recording device, and recreate the photo, the photon within the recording device. By that time the electron would be gone. You would never get a second glimpse of the same electron.
Your field of view is going to be to small compared to the distance from the electron being filmed and the recording device. The time it takes the electrons bringing the information is going to be longer then the field of view is going to be able to capture the electrons presence. So you are guaranteed to never get a second glimpse. Even if you could get one glimpse.
I was taught that infinite just meant that in one lifetime one human could not count or positively verify the occurrence, whether it be the number of particles, the length of the object, the location of the object, or whatever cannot be confirmed by one individual.
Part of the race in the Olympics where they hand off the baton from one runner to the next, is part of this proof of infinity. Or when you whisper a predetermined statement from one student to the next in a room.
All to often this exchange of information and responsibility causes error. And in science there can be no error. So one individual would have to work on the counting or tallying for a truly scientific experiment.
That is why I am an amateur scientist. In this world with the current poor labelling or mislabeling of important things, I am surely only an amateur scientist, until I get it straightened out.
If you look at the individual runner they will almost never drop a baton as they are running alone. You will almost always see the error caused while exchanging information or the baton.
Sincerely,
William McCormick