Difference between revisions of "Fundamental Theorem of Sato"
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The Fundamental Theorem of Sato states the following: | The Fundamental Theorem of Sato states the following: | ||
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Proof: | Proof: | ||
| − | Method 1: Proof by | + | Method 1: Proof by Contradiction |
Assume, for contradiction, that Sato is not amazing. | Assume, for contradiction, that Sato is not amazing. | ||
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Method 3: Proof by Pigeonhole | Method 3: Proof by Pigeonhole | ||
| − | There is only one Sato. By Pigeonhole, either Sato is amazing or he isn't. Fortunately, Sato cannot fit in a pigeonhole; hence, Sato is amazing. | + | There is only one Sato. By Pigeonhole, either Sato is amazing or he isn't (in this case, Sato goes in the unamazing pigeonhole). Fortunately, Sato cannot fit in a pigeonhole; hence, Sato is amazing. (Proved) |
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| + | Method 4: Proof by Gmass | ||
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| + | Gmass is Sato in cat form. Since Gmass is amazing, and since if <math>a=b</math> and <math>b=c</math>, <math>a=c</math>, Sato is amazing. | ||
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| + | ------ | ||
| + | Learn about Sato: | ||
| + | https://artofproblemsolving.com/wiki/index.php/Naoki_Sato | ||
| + | ------- | ||
| + | Back to Main Page: | ||
| + | https://artofproblemsolving.com/wiki/index.php/Main_Page | ||
| + | -------- | ||
Revision as of 06:47, 15 September 2020
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The Fundamental Theorem of Sato states the following:
Sato is amazing.
Proof:
Method 1: Proof by Contradiction
Assume, for contradiction, that Sato is not amazing.
This is absurd. Therefore, Sato is amazing. (Proved)
Method 2: Proof by Authority
Whatever AoPS says is correct, and AoPS says that Mr. Sato is amazing. Thus, Mr. Sato is amazing. (Proved)
Method 3: Proof by Pigeonhole
There is only one Sato. By Pigeonhole, either Sato is amazing or he isn't (in this case, Sato goes in the unamazing pigeonhole). Fortunately, Sato cannot fit in a pigeonhole; hence, Sato is amazing. (Proved)
Method 4: Proof by Gmass
Gmass is Sato in cat form. Since Gmass is amazing, and since if 
and 
, 
, Sato is amazing.
Learn about Sato: https://artofproblemsolving.com/wiki/index.php/Naoki_Sato
Back to Main Page: https://artofproblemsolving.com/wiki/index.php/Main_Page
