Euclid 2

Question 1

each line is composed of infinite points (of either 0 or finite length). If it’s zero length, then the line has no length (0+0+0+0=0). If it’s finite length, then the line has an infinitely equal amount of finite lengths; therefore infinite in length.

Answer 1

Paradox of Plurality

Question 2

both odd and even sets of numbers paired one-to-one with natural numbers. the size of the even numbers is the same cardinality as the size of the odd numbers.

Answer 2

Denumerable Sets

Question 3

There are infinitely many natural numbers; even and odd integers are a subset of them. But these subsets are the same size as the superset. (This wouldn’t be with finite sets)

Answer 3

Strangeness of the Infinite

Question 4

The length of a line is not determined by the sum of its points. Length is an additional property over and above the points. There’s an additional metric property needed.

Answer 4

Real Lines