"identically zero" meaning in English

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      "expansion": "identically zero (not comparable)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
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      "examples": [
        {
          "text": "If a holomorphic function f(z) approaches zero as z#x5C;to#x5C;infty, then f is identically zero.",
          "type": "example"
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      "glosses": [
        "Being equal to the zero function and not merely zero at a particular point in its domain."
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      "raw_glosses": [
        "(mathematics, of a function) Being equal to the zero function and not merely zero at a particular point in its domain."
      ],
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        "of a function"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
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  "word": "identically zero"
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  "lang_code": "en",
  "pos": "adj",
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      "glosses": [
        "Being equal to the zero function and not merely zero at a particular point in its domain."
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        "(mathematics, of a function) Being equal to the zero function and not merely zero at a particular point in its domain."
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