1. Cantor wondered whether there are infinities of different sizes between these two infinities.

2. Cantor's transfinite numbers orders and counts all non-genuine infinities

3. Remember, of course, that we need the round parentheses, not including the infinities.

4. Alan Lightman’s new book explores the riddles of origins, infinities, and other Bafflements brought to us by modern science

5. Alan Lightman’s new book explores the riddles of origins, infinities, and other Bafflements brought to us by modern science

6. Pondering the unknowable Alan Lightman's new book explores the riddles of origins, infinities, and other Bafflements brought to us by modern science.

7. At higher orders in the series infinities emerged, making such computations meaningless and casting serious doubts on the internal consistency of the theory itself.

8. For Kronecker, Cantor's hierarchy of infinities was inadmissible, since accepting the concept of actual infinity would open the door to paradoxes which would challenge the validity of mathematics as a whole.