Is the distance between two points infinite?

Question

After all you can divide such distance an infinite number of time right?

Answer 1

Any finite distance can be divided an infinite number of times, that doesn't make it infinite.

Answer 2

Depends on your unit of measurement. If you are willing to divide the distance an infinite number of times, then yes, there are an infinite number of infinitely small distances between any two points that are not identical.

Answer 3

This question is ancient. Look up Zeno of Elea.

What the question demonstrates is that while it might be true that math and logic apply to all the world, it is not true that ALL of math and logic apply to the world.

It does make sense to say that, in purely mathematical and logical terms, a line is infinitely divisible. But, even more obviously, this does not apply to the world outside of math and logic - it it did, there could be no such thing as motion from one place to another, because all distances would be infinite.

Obviously motion is possible, distances are not infinite, and so this aspect of math and logic does not apply to the world.

Answer 4

Although you can divide the distance an infinite number of times you cannot multiply that value an infinite number of times without exceeding your value limit. Accordingly, there is a finite value that is reached and a finite answer to your question.

I commend you for your thinking, but it only considers a portion of the whole picture. As if to say if A=B, then B must be = to A. And that concept may or may not be true.

Answer 5

Think about it this way: if you identify two points, say the two corners of your block, you know that you can walk from the one corner to the other. Therefore, we conclude, the distance between the two corners is a definite distance.

Now, if you think about walking halfway down the block, then half the remaining distance, then half again, and just keep going half the distance, it seems apparent that you will never reach the other corner. Please note, it is impossible or near impossible to really walk this way. I don't think I can judge distances well enough to walk say, an eighth of an inch or a sixteenth of an inch.

This apparent paradox illustrates the differences between points and lines. A line is a distance between two points; a point is a location in space-time. Points are on a line, but points do not form a line; lines and points are very different, though related things.

Answer 6

It's the old, 'you can move half way to your destination an infinite amount of times' questions.

But that does not work.

If you have point A and point B - you have to bear in mind that there are still other points out there that cannot be ignored.

Also, Calculus would have a way to integrate the distance between points.

Answer 7

the distance between 2 points is finite, not infinite. and no you can't divide it an infinite number of times, eventually it's done.