Paradoxes and Wonders of Infinity: Mathematical Concepts
Explore Cantor's Diagonal Argument, Hilbert's Hotel, and Gabriel's Horn in this educational guide to the different sizes and paradoxes of infinity.
Cantor's Diagonal
Argument
Assume list of decimals
Change nth digit
New number not on list
Hilbert's
Hotel
Infinite rooms
"Full" hotel
Still room for more
Infinity in
Calculus
Limits → ∞
Infinite series
Improper integrals
Gabriel's
Horn
Infinite surface area
Finite volume
"Fillable but unpaintable"
Sizes of
Infinity
Countable < uncountable
Continuum
Even bigger infinities exist
Why Infinity
Matters
Defines real numbers
Used in physics
Used in computer science
A Question to
Think About
Which infinity does the universe use?
- mathematics
- infinity
- calculus
- set-theory
- education
- paradoxes
- cantor
- hilbert