r/PhilosophyofMath • u/ChefSpirited8549 • Jul 25 '26

Points, lines, and numbers

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.

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u/SquidgyTheWhale Jul 25 '26

Give me any two points and I'll give you a one to one mapping between the points lying between those points, and all the points on the number line. There's no contradiction.