Buzz Lightyear famously shouted ‘to infinity and beyond!’ before he did anything, regardless of its size. But we all know there isn’t a ‘beyond’ because infinity always has that covered. Or does it? Patrick Honner opened his Quantized Academy article on the concept (remember, it’s not a number) with something similar:
At the end of the Marvel blockbuster Avengers: Endgame, a pre-recorded hologram of Tony Stark bids farewell to his young daughter by saying, “I love you 3,000.” The touching moment echoes an earlier scene in which the two are engaged in the playful bedtime ritual of quantifying their love for each other. According to Robert Downey Jr., the actor who plays Stark, the line was inspired by similar exchanges with his own children.
The game can be a fun way to explore large numbers:
“I love you 10.”
“But I love you 100.”
“Well, I love you 101!”
This is precisely how “googolplex” became a popular word in my home. But we all know where this argument ultimately leads:
“I love you infinity!”
“Oh yeah? I love you infinity plus 1!”
You might know that some sets of numbers are infinitely large, but did you know that some infinities are bigger than others? And that we’re not sure if there are other infinities sandwiched between the two we know best? Mathematicians have been pondering this second question for at least a century, and some recent work has changed the way people think about the issue.
Without any proofs, I had posited that there were infinities between finite numbers such as 0 and 1, and that they were maybe part of The OG Infinity. But there are bigger ones out there. What a concept!