Art of Problem Solving

Fundamental Theorem of Sato: Difference between revisions

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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. Fortunately, Sato cannot fit in a pigeonhole; hence, Sato is amazing. (Proved)

Revision as of 19:29, 23 April 2019

The Fundamental Theorem of Sato states the following:

Sato is amazing.

Proof:

Method 1: Proof by Contradiciton

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. Fortunately, Sato cannot fit in a pigeonhole; hence, Sato is amazing. (Proved)