1 cube, 2 cubes, 3 cubes, 4 cubes, 5 cubes, 6 … A mountain of cubes. Where is the boundary between an N-th number and an indeterminate set?

2 Answers

1. There is a good children's puzzle for understanding some aspects of the finite and infinite: “The runner moves 10 times faster than the turtle and is a hundred meters away from it. As long as he runs 100 meters, it will crawl 10, as long as he runs another 10 – it will crawl a meter, another meter – another decimeter, and so on. Does this mean that the runner will never catch up with her?”

   Of course it doesn't! However, we can construct a sequence of moves in which the runner is always behind.

   It's the same with dice. You can add one cube at a time and count them, so that you will never get a “Mountain”, or you can take and throw a handful or bag of cubes and immediately call them a Mountain, even if there will be much less than you COUNTED in the previous experiment. So it is only a question of perception and the concept of how this “structure”was formed.

   Log in to Reply

2. In this particular case, the boundary is “……..”

   I think that in other cases, the border will pass exactly where we put it. Namely, for the last object we defined. That is, the boundary here is an absolutely subjective value.

   If we say where this boundary is objectively located, then if we accept the thesis that all thoughts are material, then we must come to the conclusion about the boundaries of the universe. But there are two things going on here:

   1. We can only work with the boundary of the observable universe, but not with its objective boundary (if one exists);

   2. According to modern scientific concepts, the universe is expanding.

   As a result, even the objective boundary�between an N-th quantity and an indeterminate set can be specific only at a specific point in time. If it exists, then it is constantly changing, and if it does not exist, then it does not exist.

   Log in to Reply