How does set theory define infinity?

Question

I am currently working on a research project for school with the title of "How does set theory define infinity?" where I am required to write an essay with a minimum word count of 6000. My current word count is around 2500. I have written an overview of how infinity have been procieved through out history up till set theory being established by Georg Cantor, and how bijection allows us to compare cardinalities of sets. I have also written about how Cantor's diagnol argument allows us to see the varing sizes of infinite sets. I am now struggling on how to take the project forwards. Should I write about how zfc axioms define set theory? or how higher cardinals are built up from aleph null? or how the continuum hypothesis is proven to be impossible to prove? or how von neumann hierarchy delivers a different way of percieving the notion of infinity. I am also having a hard time trying to come up with a satsifactory conclusion as the topic does'nt seem to have an end.