How big is infinity? - Dennis Wildfogel
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it as an intuitive introduction to infinite sets, bijections and Cantor's results for people puzzled by different sizes of infinity.
Recommended by 3 people across 3 different months, 2014 to 2025.
What it is
A 7-minute animated TED-Ed lesson by Dennis Wildfogel that uses basic set theory to explain different sizes of infinity, including bijections, countable and uncountable sets, and Cantor's diagonal argument. It ends by noting how this leads to questions mathematics cannot answer.
What people said
Recommends goblin GONE · 2015-03 · Mathematics Stack Exchange · on “If $dx$ is an infinitesimal, can't you list all real numbers as the sequence each whole number times dx?”
@veta, check out this [this video] video to learn a few basic facts. But note that some of the stuff that is said after $8:30$ is kind of incorrect. A little bit. This [LINK] is also good stuff.
Recommends cansomeonehelpmeout · 2020-03 · Mathematics Stack Exchange · on “What formal mathematical terms are used to talk about different scales of infinity?”
This [this video] is a great video to start at to get an intuition for infinite sets and bijections. Spoiler alert, a beautiful result due to Cantor is shown here.
Recommends Winston Wolf · 2025-03 · Mathematics Stack Exchange · on “Does a line have more points than a line segment?”
No. They both have uncountably infinite points. You can think of a line is like real numbers, in which points are like specific real numbers, and they are uncountably infinite, ie, there isn't a one-to-one function from natural numbers to real numbers. Same goes for the subset of real numbers, eg, there are more real numbers between 0 and 1 than natural numbers. They are on the same scale of infinity, their cardinality [LINK] is $\mathfrak c$ , called the cardinality of the continuum [LINK] . There is a great video which helped me grasp the concept of infinity years ago: [this video] Related concepts: [LINK] [LINK]
Cites Mikky Davey · 2014-04 · Mathematics Stack Exchange · on “one to one positive integers and positive rationals”
How would you go about proving that there is a 1 : 1 correspondence between the set of positive integers and the set of positive rationals. I know there are a lot of ways to do this but I am looking for one in particular that I learned a few semesters ago. It has something to do with countability and i remember using diagonal lines. I did some searching through the resources left on my blackboard form the class and found this video. the part i am talking about starts at 2:10 [this video] Looking for help or even online resources about how you would write a proof like this out.( maybe not even write the proof but just properly explain it in written form) If anyone has any suggestions I would appre