Conversation

Oct 20, 2020

kinda fucked up how there are apparently "more" integers than there are perfect squares despite there being a demonstrably equal (infinite) number of both. 1 = 1 * 1 2 * 2 = 4 3 * 3 = 9 4 = 2 * 2 5 * 5 = 25 6 * 6 = 36 7 * 7 = 49 8 * 8 = 64 9 = 3 * 3 ...

QC (in Berlin 7/29-??? w/ COVID

)

@QiaochuYuan

Oct 20, 2020

it depends on what you mean by “more”! the squares have e.g. natural density 0 which is a decent way to formalize the intuitive idea that they get more and more sparse “more” can just mean a lot of things. there’s a reason my math blog is called “annoying precision”