Actual Infinity in Reality?

[polymath257]

Why do you assume there is a point just before 1? In fact, I can prove that, in fact, there is no point that is the 'last point before 1'.

The proof is a simple one done via proof by contradiction. Suppose x is any point before 1, so x<1. Let y be the average of x and 1. Then x<y<1, showing x is NOT the last point. hence, no last point can exist.

We cannot 'reach the destination' IN THAT WAY. We still reach the destination, but not via stopping at each of those infinitely many points.

I'm not saying that you have to stop at the point. Passing  through is fine.  

Your demonstration did not offer a rebuttal, but further re-enforces my point.  This is exactly what I was saying. 

It's your own point that you are saying there is a contradiction with, even though you keep saying that there is no contradictions.  This is why myself and Steve are saying that you will never reach the destination of 1. 

This is using the same reasoning that you used to say that there is an infinite number of points, and showing that by that reasoning you cannot reach the destination.


Now if you would want to get into what you are calling an assumption that there is a point prior to our destination (A) where it is (!A); we can work through that.  However any way you get around this, I believe is going to cause you to abandon your model which is giving you an infinite number of "points".

The contradiction is to the assumption that there is a last number before 1. That was a proof that there is not.

This is called a proof by contradiction. You assume something, get a contradiction, and thereby show it is false. In this case, the assumption was that there is a last number before 1. There isn't. But there is no reason to think there would be.

Your article was just hilarious in the complete lack of understanding of math contained in it. It assumes that infinite quantities act the same as finite. They don't. But there is no *logical* contradiction to aleph_0 +aleph_0 =aleph_0, as claimed.

At no point do we ever get a contradiction: a proof of both some statement and its negation.

It is just true.