See infinite series on Wiktionary
{
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"form": "infinite series",
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"lang_code": "en",
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"name": "Infinity",
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"examples": [
{
"text": "In 1734, Leonhard Euler solved the Basel problem by summing the infinite series #x5C;textstyle#x5C;frac#x7B;1#x7D;#x7B;1²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;2²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;3²#x7D;#x2B;#x5C;cdots#x3D;#x5C;sum#x5F;#x7B;n#x3D;1#x7D;#x7B;#x5C;infty#x7D;#x5C;frac#x7B;1#x7D;#x7B;n²#x7D;#x3D;#x5C;frac#x7B;#x5C;pi²#x7D;#x7B;6#x7D;.",
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],
"glosses": [
"Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers."
],
"id": "en-infinite_series-en-noun-hOGQx4m3",
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"(mathematical analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers."
],
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"translations": [
{
"code": "da",
"lang": "Danish",
"sense": "infinite series",
"word": "uendelig række"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "mugenkyūsū",
"sense": "infinite series",
"word": "無限級数"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "infinite series",
"tags": [
"feminine"
],
"word": "serie infinită"
},
{
"code": "ru",
"lang": "Russian",
"roman": "beskonéčnyj rjad",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "бесконе́чный ряд"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "beskonačni red"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "infinite series",
"word": "awangganing dalayray"
}
]
}
],
"word": "infinite series"
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"text": "In 1734, Leonhard Euler solved the Basel problem by summing the infinite series #x5C;textstyle#x5C;frac#x7B;1#x7D;#x7B;1²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;2²#x7D;#x2B;#x5C;frac#x7B;1#x7D;#x7B;3²#x7D;#x2B;#x5C;cdots#x3D;#x5C;sum#x5F;#x7B;n#x3D;1#x7D;#x7B;#x5C;infty#x7D;#x5C;frac#x7B;1#x7D;#x7B;n²#x7D;#x3D;#x5C;frac#x7B;#x5C;pi²#x7D;#x7B;6#x7D;.",
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"(mathematical analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers."
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{
"code": "da",
"lang": "Danish",
"sense": "infinite series",
"word": "uendelig række"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "mugenkyūsū",
"sense": "infinite series",
"word": "無限級数"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "infinite series",
"tags": [
"feminine"
],
"word": "serie infinită"
},
{
"code": "ru",
"lang": "Russian",
"roman": "beskonéčnyj rjad",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "бесконе́чный ряд"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "infinite series",
"tags": [
"masculine"
],
"word": "beskonačni red"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "infinite series",
"word": "awangganing dalayray"
}
],
"word": "infinite series"
}
Download raw JSONL data for infinite series meaning in All languages combined (2.5kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.