Art of Problem Solving

Fundamental Theorem of Sato: Difference between revisions

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This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight. This is a great time for this thread. Us glorious raiders have returned after a fortnight.
The Fundamental Theorem of Sato states the following:


Failure to listen to us may result in more raids in the future. Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.Failure to listen to us may result in more raids in the future.
'''Sato is amazing.'''


Here are the things you must surrender:
Proof:


This thread
Method 1: Proof by Contradiction
Loyalty to GMAAS


You can do it! Surrender to the glorious raiders!
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)

Latest revision as of 15:50, 28 January 2024

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)