NNG4
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Power World 10 uses ≠ which we don't yet know
Power World 10 (Fermat's Last Theorem) is mostly pretty careful to frame it entirely in language we know: (a+1) instead of (n>0), etc. But it doesn't quite finish the job: it uses the symbol ≠, which we've never seen before unless we've digressed at least to Implication World 8. An unfamiliar symbol that we don't know how to manipulate, even a fairly common-sense one, undercuts the message that the tools we now have are enough to express big problems.
My current thought on how to improve this would be to
- In the level explanation part of the text, mention that the symbol is new, but can for now be read in a common-sense way.
- In the congratulations part of the text, along with the "go read Mathematics in Lean" suggestion, add an alternative of going to Implication World (if we haven't yet) to learn about ≠, and to work up to ≤ World where we'll have the full language to restate the problem more clearly.
- (Future) If there's ever another world that depends on Power World and ≤ World, include in it a level showing how much more clearly we can now restate Fermat's Last Theorem.
Other strategies I've considered, but don't like as much, include
- Try to restate the theorem without ≠ (and without →).
- Try to explain Lean's symbol ≠ within the level text.
- Make this level depend on Implication World.