Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    If the Fundamental Theorem of Arithmetic requires proof, ... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→FACTORIZATION is in NP ∩ coNP.

    If the Fundamental Theorem of Arithmetic requires proof, then the coNP certificate argument embeds an unacknowledged mathematical assumption that could fail in alternative number-theoretic frameworks.

    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

    Sign in or register to share your perspective on this statement.

    Key Terms

    Embed(in mathematical structures)
    To fit or contain something as a part of a larger whole, like placing smaller Russian dolls inside a bigger one.
    Fundamental Theorem of Arithmetic(as a mathematical principle)
    A mathematical rule stating that every whole number greater than 1 can be broken into prime numbers in exactly one way, and no other way works.
    Mathematical assumption(as used in mathematics and epistemology)
    A basic belief or starting point that mathematicians use without proving it, which they rely on to build other mathematical ideas.
    Number-theoretic frameworks(as used in mathematics and philosophy of mathematics)
    Different possible systems or ways of thinking about numbers and how they work, which might have different rules than the traditional number system we normally use.

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    coNP certificate(as used in computational complexity theory)
    A piece of evidence or information in computer science that can quickly verify a negative answer to a problem (like proving something is NOT true), similar to how a receipt proves you bought something.
    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.
    proof(Frege's formal system; the definition still used by logicians today)
    Any finite sequence of statements such that each statement is either an axiom of the formal system or follows from previous members of the sequence by a valid rule of inference.

    Connections

    1 linked claim · 2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked
    FACTORIZATION is in NP ∩ coNP.

    Related

    FACTORIZATION is in NP ∩ coNP.

    Details

    Type
    claim
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective