Suppose for every post I make I choose a random topic, and for each new topic I gain a new follower. Then after every ten posts, one random follower of mine decides I'm not relevant enough to their interests and unfollows me. After an infinite amount of posts, will I have scared off all my followers?

#mathematics
#stochastic
#supertasks

@ausrine No, you would have scared 10% of your followers. Take p as the number of posts, and n the number of followers, where p,n ∈ ℕ₀, then the number of followers is given by n = p - ⌊p / 10⌋. If you want to determine how the amount of followers changes with posts, you can take the function n/p and see its behavior. As p grows, the ratio will be less noticeable.

See image for graph from 1-500 posts, as well as tables showing the ratios every 10 posts and how they change. This is not a mathematical proof.

@existential_wormhole I love that you took the time to give a serious answer. There are a few ways my post could be interpreted. Yours is a good one. We could also ask what the space of topics looks like. If it's finite, or at least if the subset of topics that fit in a toot is, then I'd run out of new topics, and therefore run out of new subscribers. My intended interpretation was based on this old video from PBS Infinite Series https://youtu.be/Sdp_V0L99sw
Stochastic Supertasks | Infinite Series

YouTube

@ausrine Thanks! Yeah I think I put more effort on answering that I would have planned, but it was a really interesting question. Also, this is the first time I use the floor function in a 'real-life' problem.

Agreed. Additionally how many followers can one have in this platform can be a limiting factor. But its definitely a good thing to assume infinity. If it works for all numbers, it will work in this finite platform!

PBS Infinite Series is amazing. I will take a look at that video.