In the modern academic practice, the question of where a particular idea came from, or whether an axiom is ontologically correct, is considered vacuous and out of scope. For the most part, you’re just handed a rulebook to play someone else’s game.
I very much had the opposite problem with Munkres's Topology or Dummit and Foote's Abstract Algebra: those authors hand you the ontological / scientific justifications for "everyday" ZFC without actually telling you the precise rules. I had to read a formal book on mathematical logic before I really understood point-set topology (at which point my misconceptions were clearly trivial confusion).
To be clear I think the standard intuitive semi-naive set theory is the correct approach for most math students. But it didn't work for me. I needed to see the axioms and formal language.
I think "if you don't you can't" does not preclude other don'ts leading to you can'ts, but "Do or you can't" means that if you Do you can, although in normal vernacular usage you are right that they are interchangeable.
This doesn't seem quite right to me:
I very much had the opposite problem with Munkres's Topology or Dummit and Foote's Abstract Algebra: those authors hand you the ontological / scientific justifications for "everyday" ZFC without actually telling you the precise rules. I had to read a formal book on mathematical logic before I really understood point-set topology (at which point my misconceptions were clearly trivial confusion).To be clear I think the standard intuitive semi-naive set theory is the correct approach for most math students. But it didn't work for me. I needed to see the axioms and formal language.
> "If you don't finish house chores, you can't play Minecraft"
is equivalent to "Do finish the house chores, or you can't play Minecraft".
And “If you don’t play Minecraft, you don’t have to finish house chores.”
"xor you can't play Minecraft" is correct :)
you sure?
I think "if you don't you can't" does not preclude other don'ts leading to you can'ts, but "Do or you can't" means that if you Do you can, although in normal vernacular usage you are right that they are interchangeable.