A number is a point on the number line. There are an infinite number of points in between any two points on the number line, no matter how close together the two points are. A line is defined as “the collection of all its points.” The same is true for the real number line. Does this mean that the existence of the real number line is a contradiction? Because you would need more than an infinite number of points to make a length of any value.
>>17025123There are different kinds of infinities. Some are larger than others.
>>17025123If you have two points a and b, the points on the corresponding line are given by a+(b-a)*k, where k is any real number. The infinity of points is the same infinity as R.
OP is so right that my mathematics textbooks just blinked out of existence due to the weight of their contradictions. It’s time to start over, math bros.
>>17025123Kermit would never say that.
Rational numbers are dense too
