Is there as many points on a 1 millimeter long line segment as there are in the entire universe?

It's mathematically the same, but you can use physics to refute it, because there's a concept of Planck length in physics, so the points in the universe are more than the points on the segments.

It can be said that there are the same amounts, because for infinite comparisons, we take the method of one-to-one reflection, (similar to the number of natural numbers and the number of positive odd numbers) can construct a one-to-one map from one dimension to two dimensions, so it can be said that there are the same number of points, and even three-dimensional, four-dimensional, and n-dimensional are possible.

For a more scientific explanation, you can refer to the description of the set potential in set theory and real variable functions, the point set potential on the length line segment is 1, and the point set potential in the whole universe is also 1, because (1) 1, these are two equal infinities, not big infinity and small infinity, that is too bad.

It's all infinite, but it's big infinity and small infinity.

The dots on any line segment are infinite, so one centimeter is as many as there are dots on a two-centimeter segment.

That is, r and r 2 are equal potentials, which is one of the basic conclusions of the real variable function.

Simple proof: Replace any real number 0 so r r 2

With his hard work, he successfully proved that a point on a straight line can correspond to a point on a plane, as well as a point in space. In this way, there were "as many points" in a 1-centimeter-long line as there were points on the Pacific Ocean, as well as in the entire interior of the Earth, and in later years, Cantor published a series of articles on this kind of "infinite set" problem, and through rigorous proof, he came to many astonishing conclusions.

There are an infinite number of points in a line segment, regardless of the length of the segment

But the infinite and the infinite cannot be compared, so it cannot be said that it is "as much".

I'm not very good at strict proofs, but can I give a less strict explanation? First, there are as many points on a line as there are points on a line segment (as illustrated by the tangent function y=tanx, where x is -2 to 2), secondly, there are as many points on a square as there are points on a plane (a complex sphere has as many points as a complex plane, and a complex sphere has as many points as a square topology), and finally it is explained that there are as many points on a square with side length 1 as there are as many points on a line segment with length 1, assuming that the points on the line segment can be represented by numbers, where a1, b1, etc. are positive integers, then there must be a point in the square ( , and it's a one-to-one correspondence, so there are as many points in a square as there are points in a segment.

Straight lines and planes are infinite ... Of course, that is infinite ...

If you want to correspond to the points one-to-one, you need a binary equation to limit the range of the x-axis of the equation according to the two endpoints of the line segment.

The question is too abstract, this is only a personal opinion, for your reference and discussion).

As for why 1, this brings us to the cosmic space theory.

It can be infinitely magnified on a point-based basis, but no matter how far it goes, it is contained in a space.

No matter how many dots, no matter how many lengths of line segments, the final result is 1.

Because there is only one universe in this world.

As many as the same, this means that there are as many points in the (0,1) interval as there are in the whole real number segment.

You can construct a one-to-one map, which says that the two sets of points are equipotential, i.e. "as many points".

Do the parallel line of the bottom edge of ABC intersects AB, AC in DE, and crosses the vertex A to do the oblique line of BC side, then, this oblique line intersects with BC and the ascending section DE at two points F, G, then you can do any slash laughing, so that the points on BC and DE correspond one by one, so there are as many points on the two line segments.