Not signed in

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

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite 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 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 sheaves 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 26th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted an entry [[algebraic number]] using text that Zoran had at [[algebraic number theory]]

   started an entry algebraic number using text that Zoran had at algebraic number theory

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJul 26th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexGot locked.

   Got locked.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 26th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI guess we have to wait then. Clearing the cache does not seem to solve this problem. This bug is new, isn't it? You have been reporting it a lot lately. Since when is this happening?

   I guess we have to wait then. Clearing the cache does not seem to solve this problem.

   This bug is new, isn’t it? You have been reporting it a lot lately. Since when is this happening?

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJul 27th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI noticed it maybe about month and half ago. Earlier locking could always be broken by force now some subclass of locking events results in the internal error page.

   I noticed it maybe about month and half ago. Earlier locking could always be broken by force now some subclass of locking events results in the internal error page.

5. • CommentRowNumber5.
   • CommentAuthorTobyBartels
   • CommentTimeJul 27th 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI added a bit about transcendental numbers.

   I added a bit about transcendental numbers.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeSep 29th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the picture from [here](https://en.wikipedia.org/wiki/File:Algebraicszoom.png) <a href="https://ncatlab.org/nlab/revision/diff/algebraic+number/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+number/4">v4</a>, <a href="https://ncatlab.org/nlab/show/algebraic+number">current</a>

   added the picture from here

   diff, v4, current

7. • CommentRowNumber7.
   • CommentAuthorTodd_Trimble
   • CommentTimeSep 29th 2018
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexProvided alternate characterizations of algebraic numbers and algebraic integers in terms of finite rank extensions. Replaced the earlier description of algebraic number fields which seemed to mandate splitting fields. <a href="https://ncatlab.org/nlab/revision/diff/algebraic+number/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+number/5">v5</a>, <a href="https://ncatlab.org/nlab/show/algebraic+number">current</a>

   Provided alternate characterizations of algebraic numbers and algebraic integers in terms of finite rank extensions. Replaced the earlier description of algebraic number fields which seemed to mandate splitting fields.

   diff, v5, current

8. • CommentRowNumber8.
   • CommentAuthorGuest
   • CommentTimeApr 17th 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexIn constructive mathematics, is a transcendental number a complex number $z\in\mathbb{C}$ that is not algebraic, or a complex number $z\in\mathbb{C}$ such that the complex norm of the difference between $z$ and every algebraic number $a\in\overline{\mathbb{Q}}\subseteq\mathbb{C}$ is positive ($\vert z - a \vert \gt 0$)?

   In constructive mathematics, is a transcendental number a complex number $z\in\mathbb{C}$ that is not algebraic, or a complex number $z\in\mathbb{C}$ such that the complex norm of the difference between $z$ and every algebraic number $a\in\overline{\mathbb{Q}}\subseteq\mathbb{C}$ is positive ($\vert z - a \vert \gt 0$)?

9. • CommentRowNumber9.
   • CommentAuthorUlrik
   • CommentTimeApr 18th 2022
   • PermaLink
   Author: Ulrik
   Format: MarkdownItexI'm not sure if/where this is discussed in the literature, but it's analogous to the situation with irrational (apart from all rational numbers) vs not rational. So I would say yes: Constructively, transcendental should mean apart from all algebraic numbers, and this is stronger than not being algebraic.

   I’m not sure if/where this is discussed in the literature, but it’s analogous to the situation with irrational (apart from all rational numbers) vs not rational. So I would say yes: Constructively, transcendental should mean apart from all algebraic numbers, and this is stronger than not being algebraic.

10. • CommentRowNumber10.
    • CommentAuthornLab edit announcer
    • CommentTimeFeb 22nd 2024
    • PermaLink
    Author: nLab edit announcer
    Format: MarkdownItexAdded requirement of polynomials being non-zero, since every number is a root of the zero polynomial Anonymouse <a href="https://ncatlab.org/nlab/revision/diff/algebraic+number/13">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+number/13">v13</a>, <a href="https://ncatlab.org/nlab/show/algebraic+number">current</a>

    Added requirement of polynomials being non-zero, since every number is a root of the zero polynomial

    Anonymouse

    diff, v13, current