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Erdős problem 846

Erdős Problem 846 Let A ⊂ ℝ² be an infinite set for which there exists some ϵ>0 such that in any subset of A of size n there are always at least ϵn with no three on a line. Is it true that A is the union of a finite number of sets where no three are on a line?

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Problem row
sha256:ca420e087e4da4a7230d8c4f0d2d9fcf5a8e3dd96fce60c693252bbb0c10e71d
Metadata
sha256:601dda0d1b5327827f293e9a1ea68fe890e3963762fe62eac31f836939fecb4d
Observation
sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
Content
sha256:68f604c6fc7b02618e031b289d3351ee3e9645bee13f286b4b8a6be941cd30b5
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
Source commit
2415f78e850aeee50afdca525c6f2e0ea606f207

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