Nitpicks: Def 2.4 builds on the obvious generalisation of Def 2.3, not Def 2.3 itself. Also, Def. 2.3 is a little poorly worded, and should make clear that “not all sets [1]all sets of reals which are bounded below have an infimum”. I think it would be helpful for those with no background in proofs if you had an exercise to justify the use of “the” when talking about the supremum of a set. Or even link it to the idea of a lower bound at all.
More to come as I read through this.
EDIT: I think you probably want to point people to guides on how to prove things so that people without maths backgrounds know what task they’re meant to be accomplishing. Otherwise they might go through this text and be hopelessly stuck or think they’ve proven something when they really haven’t. Plus, having the ability to notice the difference between a proof and the intuition behind a proof is quite important for doing mathsy stuff, and Vanessa’s agenda is amongst the more mathy alignment agendas.
Nitpicks: Def 2.4 builds on the obvious generalisation of Def 2.3, not Def 2.3 itself. Also, Def. 2.3 is a little poorly worded, and should make clear that “
not all sets[1]all sets of reals which are bounded below have an infimum”. I think it would be helpful for those with no background in proofs if you had an exercise to justify the use of “the” when talking about the supremum of a set. Or even link it to the idea of a lower bound at all.More to come as I read through this.
EDIT: I think you probably want to point people to guides on how to prove things so that people without maths backgrounds know what task they’re meant to be accomplishing. Otherwise they might go through this text and be hopelessly stuck or think they’ve proven something when they really haven’t. Plus, having the ability to notice the difference between a proof and the intuition behind a proof is quite important for doing mathsy stuff, and Vanessa’s agenda is amongst the more mathy alignment agendas.
Ignore the struck through text.
Do you mean ‘all sets of reals which are bounded below DO have an infimum’?
Thanks, fixed.