or 16 subsets; the power set of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} contains 210or 1024 subsets; and the power set of {1, 2, 3, 4… 100} contains 2100or 1,267,650,600,228,229,401,496,703,205,376 subsets, which is more than one million trillion! Using the means of the power set, “any finite set can be used as a stepping stone to build another much larger, finite set” (p. 16).Cantor continued even further with his discoveries as he proved that one-dimensional space (a line) has exactly the same number of points as two-dimensional space. Carrying this further, we now know that two- and three-dimensional spaces also have the same number of points, which inturn means that one- and three-dimensional spaces have the same number of points. By using thisinformation, we can honestly conclude that there are infinitely-dimensional spaces, and these canall interact and have the same as our three-dimensional world.

All of these discoveries have proved that Cantor has changed the “mathematical landscapeby his inquiries into the infinite” (p. 23) and he’s proven that “human intuition has little authority” (p.23) when it comes to infinity. He changed the verb of “interminable process” to a noun of “actual entity” when it comes to mathematicians use of “infinity.”