"transfinitely" meaning in English

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  "etymology_text": "From transfinite + -ly.",
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  "lang_code": "en",
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      "word": "finitely"
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          "ref": "1999, Thomas Strahm, “First Steps into Metapredictivity in Explicit Mathematics”, in S. Barry Cooper, John K. Truss, editors, Sets and Proofs, Cambridge University Press, page 399:",
          "text": "We finish this section by briefly addressing how the reduction procedure for #92;mathsf#123;EMU#125; described so far can be formalized in the transfinitely iterated fixed point theory #92;widehat#123;#92;mathsf#123;ID",
          "type": "quote"
        },
        {
          "ref": "2003, Thomas Forster, Logic, Induction and Sets, Cambridge University Press, page 147:",
          "text": "After we have performed the deletion operation infinitely many times, we can look at what is left and perform the deletion operation on that, and thereby continue the process transfinitely.",
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      "glosses": [
        "In a manner that requires a transfinite number of steps."
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        "(manner) In a manner that requires a transfinite number of steps."
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        "not-comparable"
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          "ref": "2004, Lisa Robin Marks, The Axiom of Choice, Berkeley: University of California, page 35:",
          "text": "The concern was voiced that Zermelo assumed transfinitely many successive choices, where one choice depends upon another, and that this was unacceptable.",
          "type": "quote"
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          "ref": "2014, Ali Sanayei, Otto E. Rössler, Chaotic Harmony: A Dialog about Physics, Complexity and Life, Springer, page 126:",
          "text": "It was very radical because he also claimed that symmetry is a feature in mathematics and reality that is not just an infinitely accurate property, but a transfinitely accurate one. Like the modern idea of fractals—where we have this Mandelbrot type thinking of everything repeating itself all over again not just infinitely many times, but in such a way that the surface around it is transfinitely large.",
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        "Of transfinite degree."
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      "raw_glosses": [
        "(degree) Of transfinite degree."
      ],
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        "not-comparable"
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  "word": "transfinitely"
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  "etymology_text": "From transfinite + -ly.",
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          "ref": "1999, Thomas Strahm, “First Steps into Metapredictivity in Explicit Mathematics”, in S. Barry Cooper, John K. Truss, editors, Sets and Proofs, Cambridge University Press, page 399:",
          "text": "We finish this section by briefly addressing how the reduction procedure for #92;mathsf#123;EMU#125; described so far can be formalized in the transfinitely iterated fixed point theory #92;widehat#123;#92;mathsf#123;ID",
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        "In a manner that requires a transfinite number of steps."
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        "(manner) In a manner that requires a transfinite number of steps."
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        "Of transfinite degree."
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        "(degree) Of transfinite degree."
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  "word": "transfinitely"
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