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Suppose x is not even . | Wiki1k:wikipedia:82285:17:0 | 0 | Suppose | true | suppose | [
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Sometimes , the abbreviation `` Q.E.D. '' is written to indicate the end of a proof . | Wiki1k:wikipedia:82285:40:0 | 8 | written | true | write | [
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Sometimes , the abbreviation `` Q.E.D. '' is written to indicate the end of a proof . | Wiki1k:wikipedia:82285:40:0 | 8 | written | true | write | [
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Sometimes , the abbreviation `` Q.E.D. '' is written to indicate the end of a proof . | Wiki1k:wikipedia:82285:40:0 | 8 | written | true | write | [
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Sometimes , the abbreviation `` Q.E.D. '' is written to indicate the end of a proof . | Wiki1k:wikipedia:82285:40:0 | 10 | indicate | true | indicate | [
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Sometimes , the abbreviation `` Q.E.D. '' is written to indicate the end of a proof . | Wiki1k:wikipedia:82285:40:0 | 10 | indicate | true | indicate | [
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This abbreviation stands for `` Quod Erat Demonstrandum '' , which is Latin for `` that which was to be demonstrated '' . | Wiki1k:wikipedia:82285:40:1 | 2 | stands | true | stand | [
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This abbreviation stands for `` Quod Erat Demonstrandum '' , which is Latin for `` that which was to be demonstrated '' . | Wiki1k:wikipedia:82285:40:1 | 2 | stands | true | stand | [
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This abbreviation stands for `` Quod Erat Demonstrandum '' , which is Latin for `` that which was to be demonstrated '' . | Wiki1k:wikipedia:82285:40:1 | 20 | demonstrated | true | demonstrate | [
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A more common alternative is to use a square or a rectangle , such as □ or ∎ , known as a `` tombstone '' or `` halmos '' after its eponym Paul Halmos . | Wiki1k:wikipedia:82285:40:2 | 6 | use | true | use | [
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A more common alternative is to use a square or a rectangle , such as □ or ∎ , known as a `` tombstone '' or `` halmos '' after its eponym Paul Halmos . | Wiki1k:wikipedia:82285:40:2 | 6 | use | true | use | [
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A more common alternative is to use a square or a rectangle , such as □ or ∎ , known as a `` tombstone '' or `` halmos '' after its eponym Paul Halmos . | Wiki1k:wikipedia:82285:40:2 | 19 | known | true | know | [
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A more common alternative is to use a square or a rectangle , such as □ or ∎ , known as a `` tombstone '' or `` halmos '' after its eponym Paul Halmos . | Wiki1k:wikipedia:82285:40:2 | 19 | known | true | know | [
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A more common alternative is to use a square or a rectangle , such as □ or ∎ , known as a `` tombstone '' or `` halmos '' after its eponym Paul Halmos . | Wiki1k:wikipedia:82285:40:2 | 19 | known | true | know | [
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Often , `` which was to be shown '' is verbally stated when writing `` QED '' , '' □ '' , or '' ∎ '' during an oral presentation . | Wiki1k:wikipedia:82285:40:3 | 7 | shown | true | show | [
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Often , `` which was to be shown '' is verbally stated when writing `` QED '' , '' □ '' , or '' ∎ '' during an oral presentation . | Wiki1k:wikipedia:82285:40:3 | 11 | stated | true | state | [
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Often , `` which was to be shown '' is verbally stated when writing `` QED '' , '' □ '' , or '' ∎ '' during an oral presentation . | Wiki1k:wikipedia:82285:40:3 | 13 | writing | true | write | [
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Further advances took place in medieval Islamic mathematics . | Wiki1k:wikipedia:82285:4:0 | 2 | took | true | take | [
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While earlier Greek proofs were largely geometric demonstrations , the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry . | Wiki1k:wikipedia:82285:4:1 | 18 | allowed | true | allow | [
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While earlier Greek proofs were largely geometric demonstrations , the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry . | Wiki1k:wikipedia:82285:4:1 | 25 | depended | true | depend | [
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In the 10th century CE , the Iraqi mathematician Al-Hashimi provided general proofs for numbers -LRB- rather than geometric demonstrations -RRB- as he considered multiplication , division , etc. for `` lines . '' | Wiki1k:wikipedia:82285:4:2 | 10 | provided | true | provide | [
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He used this method to provide a proof of the existence of irrational numbers . | Wiki1k:wikipedia:82285:4:3 | 1 | used | true | use | [
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He used this method to provide a proof of the existence of irrational numbers . | Wiki1k:wikipedia:82285:4:3 | 1 | used | true | use | [
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Alhazen also developed the method of proof by contradiction , as the first attempt at proving the Euclidean parallel postulate . | Wiki1k:wikipedia:82285:4:5 | 2 | developed | true | develop | [
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The first component corresponds to sensible heat and the second to latent heat . | Wiki1k:wikipedia:8282374:24:1 | 3 | corresponds | true | correspond | [
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The Canadian Hurricane Center -LRB- CHC -RRB- issues advisories on hurricanes and their remnants for Canadian citizens when they affect Canada . | Wiki1k:wikipedia:8282374:36:3 | 19 | affect | true | affect | [
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The Canadian Hurricane Center -LRB- CHC -RRB- issues advisories on hurricanes and their remnants for Canadian citizens when they affect Canada . | Wiki1k:wikipedia:8282374:36:3 | 19 | affect | true | affect | [
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Intense tropical cyclones pose a particular observation challenge , as they are a dangerous oceanic phenomenon , and weather stations , being relatively sparse , are rarely available on the site of the storm itself . | Wiki1k:wikipedia:8282374:57:0 | 3 | pose | true | pose | [
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For this reason , there are teams of meteorologists that move into the path of tropical cyclones to help evaluate their strength at the point of landfall . | Wiki1k:wikipedia:8282374:57:3 | 18 | help | true | help | [
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