Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: natural number

Bottom of Page

1 to 8 of 8

  1.  

  1. Add forgotten +1

    RichardMau5

    diff, v25, current

    • 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.)

    diff, v27, current

    • 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

    diff, v28, current

    • 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⊂ℕS \subset \mathbb{N} with SS inhabited implies that the subset SS contains its minimum, then LEM holds.

  7. if zero is not in the natural numbers then the natural numbers do not form a rig.

    Anonymous

    diff, v31, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeFeb 7th 2023

    added pointer to:

    diff, v36, current

1 to 8 of 8

  1.