See fundamental theorem in All languages combined, or Wiktionary
Download JSON data for fundamental theorem meaning in English (3.6kB)
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{
"ref": "1994, Joseph E. Stiglitz, Whither Socialism?, The MIT Press, page 27",
"text": "In this and the next chapter I return to the fundamental theorems of welfare economics. In this chapter I argue that the first fundamental theorem of welfare economics—asserting the efficiency of competitive economics—is fundamentally flawed.",
"type": "quotation"
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{
"ref": "2010, Vasily E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, page 247",
"text": "The first fundamental theorem of calculus states that the differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is obtained[…].",
"type": "quotation"
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{
"ref": "2012, Joseph L. Taylor, Foundations of Analysis, American Mathematical Society, page 114",
"text": "There are two fundamental theorems of calculus. Both relate differentiation to integration. In most calculus courses, the Second Fundamental Theorem is usually proved first and then used to prove the First Fundamental Theorem. Unfortunately, this results in a First Fundamental Theorem that is weaker than it could be.",
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"(chiefly mathematics) A theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field."
],
"related": [
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"word": "fundamental lemma"
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"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "fundamental theorem",
"tags": [
"masculine"
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"word": "teorema fonamental"
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"sense": "fundamental theorem",
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{
"code": "eo",
"lang": "Esperanto",
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"word": "fundamenta teoremo"
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{
"code": "fr",
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"sense": "fundamental theorem",
"tags": [
"masculine"
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"word": "théorème fondamental"
},
{
"code": "de",
"lang": "German",
"sense": "fundamental theorem",
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"masculine"
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"word": "Fundamentalsatz"
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{
"code": "de",
"lang": "German",
"sense": "fundamental theorem",
"tags": [
"masculine"
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"word": "Hauptsatz"
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{
"code": "it",
"lang": "Italian",
"sense": "fundamental theorem",
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"masculine"
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"word": "teorema fondamentale"
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{
"code": "la",
"lang": "Latin",
"sense": "fundamental theorem",
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"word": "theōrēma fundāmentāle"
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{
"code": "pt",
"lang": "Portuguese",
"sense": "fundamental theorem",
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"word": "teorema fundamental"
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"lang": "Spanish",
"sense": "fundamental theorem",
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"word": "teorema fundamental"
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"wikipedia": [
"fundamental theorem"
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"word": "fundamental theorem"
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"examples": [
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"ref": "1994, Joseph E. Stiglitz, Whither Socialism?, The MIT Press, page 27",
"text": "In this and the next chapter I return to the fundamental theorems of welfare economics. In this chapter I argue that the first fundamental theorem of welfare economics—asserting the efficiency of competitive economics—is fundamentally flawed.",
"type": "quotation"
},
{
"ref": "2010, Vasily E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, page 247",
"text": "The first fundamental theorem of calculus states that the differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is obtained[…].",
"type": "quotation"
},
{
"ref": "2012, Joseph L. Taylor, Foundations of Analysis, American Mathematical Society, page 114",
"text": "There are two fundamental theorems of calculus. Both relate differentiation to integration. In most calculus courses, the Second Fundamental Theorem is usually proved first and then used to prove the First Fundamental Theorem. Unfortunately, this results in a First Fundamental Theorem that is weaker than it could be.",
"type": "quotation"
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"(chiefly mathematics) A theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field."
],
"topics": [
"mathematics",
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"wikipedia": [
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"translations": [
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"code": "ca",
"lang": "Catalan",
"sense": "fundamental theorem",
"tags": [
"masculine"
],
"word": "teorema fonamental"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "fundamental theorem",
"tags": [
"feminine"
],
"word": "hoofdstelling"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "fundamental theorem",
"word": "fundamenta teoremo"
},
{
"code": "fr",
"lang": "French",
"sense": "fundamental theorem",
"tags": [
"masculine"
],
"word": "théorème fondamental"
},
{
"code": "de",
"lang": "German",
"sense": "fundamental theorem",
"tags": [
"masculine"
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"word": "Fundamentalsatz"
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{
"code": "de",
"lang": "German",
"sense": "fundamental theorem",
"tags": [
"masculine"
],
"word": "Hauptsatz"
},
{
"code": "it",
"lang": "Italian",
"sense": "fundamental theorem",
"tags": [
"masculine"
],
"word": "teorema fondamentale"
},
{
"code": "la",
"lang": "Latin",
"sense": "fundamental theorem",
"tags": [
"neuter"
],
"word": "theōrēma fundāmentāle"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "fundamental theorem",
"tags": [
"masculine"
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"word": "teorema fundamental"
},
{
"code": "es",
"lang": "Spanish",
"sense": "fundamental theorem",
"tags": [
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"word": "teorema fundamental"
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"word": "fundamental theorem"
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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.
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