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nLab > Latest Changes: algebraic number

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2011

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

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJul 26th 2011

    Got locked.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2011

    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?

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeJul 27th 2011

    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.

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeJul 27th 2011

    I added a bit about transcendental numbers.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeSep 29th 2018

    added the picture from here

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 29th 2018

    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

    • CommentRowNumber8.
    • CommentAuthorGuest
    • CommentTimeApr 17th 2022

    In constructive mathematics, is a transcendental number a complex number z∈ℂz\in\mathbb{C} that is not algebraic, or a complex number z∈ℂz\in\mathbb{C} such that the complex norm of the difference between zz and every algebraic number a∈ℚ¯⊆ℂa\in\overline{\mathbb{Q}}\subseteq\mathbb{C} is positive (|z−a|>0\vert z - a \vert \gt 0)?

    • CommentRowNumber9.
    • CommentAuthorUlrik
    • CommentTimeApr 18th 2022

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

    Anonymouse

    diff, v13, current

1 to 10 of 10

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