[Merged by Bors] - doc(MetricSpace/Hausdorff): style fixes in doc comments #9856
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grunweg
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| theorem infDist_le_hausdorffDist_of_mem (hx : x ∈ s) (fin : hausdorffEdist s t ≠ ⊤) : | ||
| infDist x t ≤ hausdorffDist s t := | ||
| toReal_mono fin (infEdist_le_hausdorffEdist_of_mem hx) | ||
| #align metric.inf_dist_le_Hausdorff_dist_of_mem Metric.infDist_le_hausdorffDist_of_mem | ||
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| /-- If the Hausdorff distance is `< r`, then any point in one of the sets is at distance | ||
| `< r` of a point in the other set -/ | ||
| /-- If the Hausdorff distance is `< r`, any point in one of the sets is at distance |
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| /-- If the Hausdorff distance is `< r`, any point in one of the sets is at distance | |
| /-- If the Hausdorff distance is `< r`, then any point in one of the sets is at distance |
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As I understand it, correct grammar doesn't require the "then". Hence, I'd like to leave this as-is.
| @@ -806,8 +806,8 @@ theorem exists_dist_lt_of_hausdorffDist_lt {r : ℝ} (h : x ∈ s) (H : hausdorf | |||
| exact ⟨y, hy, yr⟩ | |||
| #align metric.exists_dist_lt_of_Hausdorff_dist_lt Metric.exists_dist_lt_of_hausdorffDist_lt | |||
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| /-- If the Hausdorff distance is `< r`, then any point in one of the sets is at distance | |||
| `< r` of a point in the other set -/ | |||
| /-- If the Hausdorff distance is `< r`, any point in one of the sets is at distance | |||
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| /-- If the Hausdorff distance is `< r`, any point in one of the sets is at distance | |
| /-- If the Hausdorff distance is `< r`, then any point in one of the sets is at distance |
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Thanks for the fast review. Indeed, this is not a PR I would create out of the blue - but as I was in the area already, that felt appropriate. |
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* End sentences with a full stop (per the style guide). * Fix grammar in a few trivial cases. * Use "triangle inequality", not "triangular inequality".
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By-product of creating module docstrings in #9809.
Reviewing this should not require deeply understanding the mathematics.
All the docstrings "is continuous in point" still read strangely to me (I'd rather write "for a fixed set s" instead); I didn't modify them.