Template:Proof: Difference between revisions

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<includeonly>{{Databox|{{{title|Proof}}}| {{{contents~~|{{{1}}}~~}}} {{qed}}}}[[Category:Articles with proofs]]</includeonly><noinclude>

<includeonly>{{Databox|{{{title|Proof}}}| {{{contents}}} {{qed}}}}[[Category:Articles with proofs]]</includeonly><noinclude>

Box for proofs. This calls [[Template: Databox]] but it automatically:

* appends [[Template: Qed]] in the end of the contents;

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{{Proof|title=Proof that <math>\sqrt{2}</math> is irrational|Assume <math>\sqrt{2}</math> is ''p''/''q'', where ''p'', ''q'' ∈ ℤ>0 and gcd(''p'', ''q'') = 1. Then ''p''2/''q''2 = 2, and ''p''2 = 2''q''2. Since ''p''2 is even, and gcd(''p'', ''q'') = 1, gcd(''p''2, ''q''2) = 1, ''q''2 must be odd. Hence ''p''2 ≡ 2 (mod 4), which is impossible because the square of an integer must always be congruent to 0 or 1 (mod 4).

{{Proof|title=Proof that <math>\sqrt{2}</math> is irrational|

contents=Assume <math>\sqrt{2}</math> is ''p''/''q'', where ''p'', ''q'' ∈ ℤ>0 and gcd(''p'', ''q'') = 1. Then ''p''2/''q''2 = 2, and ''p''2 = 2''q''2. Since ''p''2 is even, and gcd(''p'', ''q'') = 1, gcd(''p''2, ''q''2) = 1, ''q''2 must be odd. Hence ''p''2 ≡ 2 (mod 4), which is impossible because the square of an integer must always be congruent to 0 or 1 (mod 4).

}}

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-<includeonly>{{Databox|{{{title|Proof}}}|<br/>{{{contents|{{{1}}}}}} {{qed}}}}[[Category:Articles with proofs]]</includeonly><noinclude>
+<includeonly>{{Databox|{{{title|Proof}}}|<br/>{{{contents}}} {{qed}}}}[[Category:Articles with proofs]]</includeonly><noinclude>
 Box for proofs. This calls [[Template: Databox]] but it automatically:
 * appends [[Template: Qed]] in the end of the contents;
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-{{Proof|title=Proof that <math>\sqrt{2}</math> is irrational|Assume <math>\sqrt{2}</math> is ''p''/''q'', where ''p'', ''q'' ∈ ℤ<sub>>0</sub> and gcd(''p'', ''q'') = 1. Then ''p''<sup>2</sup>/''q''<sup>2</sup> = 2, and ''p''<sup>2</sup> = 2''q''<sup>2</sup>. Since ''p''<sup>2</sup> is even, and gcd(''p'', ''q'') = 1, gcd(''p''<sup>2</sup>, ''q''<sup>2</sup>) = 1, ''q''<sup>2</sup> must be odd. Hence ''p''<sup>2</sup> ≡ 2 (mod 4), which is impossible because the square of an integer must always be congruent to 0 or 1 (mod 4).
+{{Proof|title=Proof that <math>\sqrt{2}</math> is irrational|
+contents=Assume <math>\sqrt{2}</math> is ''p''/''q'', where ''p'', ''q'' ∈ ℤ<sub>>0</sub> and gcd(''p'', ''q'') = 1. Then ''p''<sup>2</sup>/''q''<sup>2</sup> = 2, and ''p''<sup>2</sup> = 2''q''<sup>2</sup>. Since ''p''<sup>2</sup> is even, and gcd(''p'', ''q'') = 1, gcd(''p''<sup>2</sup>, ''q''<sup>2</sup>) = 1, ''q''<sup>2</sup> must be odd. Hence ''p''<sup>2</sup> ≡ 2 (mod 4), which is impossible because the square of an integer must always be congruent to 0 or 1 (mod 4).
 }}
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