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    A course in mathematical analysis / by Garling, D. J. H.

    Published 2013
    Subjects: “…Metric spaces. 9797…”
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    Book
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    Emergence of Self-Identity in Artificial Intelligence: A Mathematical Framework and Empirical Study with Generative Large Language Models by Minhyeok Lee

    Published 2025-01-01
    “…Our framework posits that self-identity emerges from two mathematically quantifiable conditions: the existence of a connected continuum of memories <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mo>⊆</mo><mi mathvariant="script">M</mi></mrow></semantics></math></inline-formula> in a metric space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">M</mi><mo>,</mo><msub><mi>d</mi><mi mathvariant="script">M</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, and a continuous mapping <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>:</mo><mi mathvariant="script">M</mi><mo>→</mo><mi mathvariant="script">S</mi></mrow></semantics></math></inline-formula> that maintains consistent self-recognition across this continuum, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">S</mi><mo>,</mo><msub><mi>d</mi><mi mathvariant="script">S</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> represents the metric space of possible self-identities. …”
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