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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

RichardMau5

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeOct 11th 2021
• (edited Oct 11th 2021)

started an Examples-section (here)

So far we have tries for 0, 1 and 24.

(We also have an entry that answers to 2, but that’s about a category, not a number – incidentally, I don’t it’s a good idea to call this category by this name, even if many authors do.)

• CommentRowNumber3.
• CommentAuthorNikolajK
• CommentTimeOct 15th 2021
• (edited Oct 15th 2021)

In Proposition 3.1., there happens the common faux pas. It currently says

If any inhabited subset of the natural numbers possesses a minimal element, then the law of excluded middle holds.

“Any” can be used for \forall, but if that word is put in an antecedent, then it becomes an \exists.

I quickly tried to search the site and there’s some other, more mildly ambiguous cases. In initial object, it says

An initial object ∅ is called a strict initial object if any morphism x→∅ must be an isomorphism.

This is an intended \forall, but I think I can construe a sentence for the same form where this would also turn to an intended \exists:

“A school class will immediately be put in quarantine if any of the kids must see a doctor.”

:P

I think those cases will always be resolved by substituting ’any’ with ’every’.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 15th 2021

Please fix it where you spot it. Thanks.

• CommentRowNumber5.
• CommentAuthorNikolajK
• CommentTimeOct 15th 2021

any=>every

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeOct 16th 2021

Thanks. By the way, since this is inside a proposition (here), one could alternatively use mathematical language, which might be preferable anyways, as in:

If $S \subset \mathbb{N}$ with $S$ inhabited implies that the subset $S$ contains its minimum, then LEM holds.