"empty sum" meaning in English

{
  "forms": [
    {
      "form": "empty sums",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "empty sum (plural empty sums)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [],
          "source": "w"
        },
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          "name": "Entries with translation boxes",
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        {
          "kind": "other",
          "langcode": "en",
          "name": "Arithmetic",
          "orig": "en:Arithmetic",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "The result of adding no numbers, conventionally defined to equal zero."
      ],
      "id": "en-empty_sum-en-noun-lfZ7CI5A",
      "links": [
        [
          "arithmetic",
          "arithmetic"
        ],
        [
          "add",
          "add"
        ]
      ],
      "raw_glosses": [
        "(arithmetic) The result of adding no numbers, conventionally defined to equal zero."
      ],
      "related": [
        {
          "word": "empty product"
        }
      ],
      "synonyms": [
        {
          "word": "nullary sum"
        }
      ],
      "topics": [
        "arithmetic"
      ],
      "translations": [
        {
          "code": "bg",
          "lang": "Bulgarian",
          "lang_code": "bg",
          "roman": "prazna suma",
          "sense": "result of adding no numbers",
          "tags": [
            "feminine"
          ],
          "word": "празна сума"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "lang_code": "fi",
          "sense": "result of adding no numbers",
          "word": "tyhjä summa"
        },
        {
          "code": "fr",
          "lang": "French",
          "lang_code": "fr",
          "sense": "result of adding no numbers",
          "tags": [
            "feminine"
          ],
          "word": "somme vide"
        },
        {
          "code": "de",
          "lang": "German",
          "lang_code": "de",
          "sense": "result of adding no numbers",
          "tags": [
            "feminine"
          ],
          "word": "Nullsumme"
        }
      ]
    }
  ],
  "word": "empty sum"
}

{
  "forms": [
    {
      "form": "empty sums",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "empty sum (plural empty sums)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "empty product"
    }
  ],
  "senses": [
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        "English countable nouns",
        "English entries with incorrect language header",
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        "English nouns",
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        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Bulgarian translations",
        "Terms with Finnish translations",
        "Terms with French translations",
        "Terms with German translations",
        "en:Arithmetic"
      ],
      "glosses": [
        "The result of adding no numbers, conventionally defined to equal zero."
      ],
      "links": [
        [
          "arithmetic",
          "arithmetic"
        ],
        [
          "add",
          "add"
        ]
      ],
      "raw_glosses": [
        "(arithmetic) The result of adding no numbers, conventionally defined to equal zero."
      ],
      "topics": [
        "arithmetic"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "nullary sum"
    }
  ],
  "translations": [
    {
      "code": "bg",
      "lang": "Bulgarian",
      "lang_code": "bg",
      "roman": "prazna suma",
      "sense": "result of adding no numbers",
      "tags": [
        "feminine"
      ],
      "word": "празна сума"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "lang_code": "fi",
      "sense": "result of adding no numbers",
      "word": "tyhjä summa"
    },
    {
      "code": "fr",
      "lang": "French",
      "lang_code": "fr",
      "sense": "result of adding no numbers",
      "tags": [
        "feminine"
      ],
      "word": "somme vide"
    },
    {
      "code": "de",
      "lang": "German",
      "lang_code": "de",
      "sense": "result of adding no numbers",
      "tags": [
        "feminine"
      ],
      "word": "Nullsumme"
    }
  ],
  "word": "empty sum"
}