Exploring Infinity with Vsauce

What is always possible, no matter how large a number you think of?

• Finding the end of numbers

• Finding a number that is smaller

• Finding a number that is larger

• Finding a number that is exactly the same

What type of number is infinity?

• A finite number

• A cardinal number

• A type of number used to describe unending amounts

• An ordinal number

What is aleph null?

• The total number of rational numbers

• A type of ordinal number

• The smallest infinity

• The largest number possible

What is the difference between cardinal and ordinal numbers?

• Cardinal numbers describe order, while ordinal numbers count things

• Cardinal numbers count things, while ordinal numbers describe order

• There is no difference; they are the same

• Ordinal numbers are always larger than cardinal numbers

How can we count past aleph null?

• By adding one to aleph null

• It's not possible to count past aleph null

• By using finite numbers

• By using the concept of supertasks

What does omega represent in mathematics?

• The total number of even numbers

• The first transfinite ordinal number

• The smallest infinity

• The largest finite number

What does the power set of aleph null represent?

• A finite set

• An infinity larger than aleph null

• An infinity exactly equal to aleph null

• A smaller infinity than aleph null

What is the continuum hypothesis?

• A hypothesis that all infinities are the same size

• A hypothesis that there is no infinity between aleph null and the power set of the naturals

• A hypothesis that infinity does not exist

• A hypothesis that all cardinal numbers are accessible

What is an inaccessible cardinal?

• The total number of natural numbers

• A cardinal number that can be reached using standard operations

• A number smaller than aleph null

• A number so large it cannot be reached from below

Why is aleph null considered an inaccessible number by some authors?

• Because it is equal to the power set of the naturals

• Because it is the largest number possible

• Because it is a finite number

• Because it cannot be reached from below using finite operations