Infinity & Sets Paradoxes

• Zeno's Paradox - To reach a destination, you must first travel half the distance, then half of what remains, forever....

• Coastline Paradox - The length of a coastline depends on the ruler size! Smaller rulers reveal more detail, making the c...

• Hilbert's Hotel - A hotel with infinite rooms, all full, can still accommodate infinitely many new guests!...

• Burali-Forti Paradox - If ordinal numbers formed a set, that set would have an ordinal number - one that is both in the set...

• Cantor's Paradox - The set of all sets would contain its own power set. But power sets are always larger than their ori...

• Galileo's Paradox - Most integers are NOT perfect squares, yet there are exactly as many perfect squares as integers! Bo...

• Thomson's Lamp - A lamp is toggled on/off at times 1, 1/2, 1/4, 1/8... After 2 minutes (infinite toggles), is it on o...

• Grandi's Series - What is 1 - 1 + 1 - 1 + 1 - 1...? Grouping differently gives 0, 1, or 1/2. All seem valid!...

• Gabriel's Horn - A trumpet shape with FINITE volume but INFINITE surface area. You can fill it with paint, but never ...