Let:
A = X-1
B = X
C = 1
C = B – A
C ( B – A ) = ( B – A )2
C B – C A = B2 – 2 A B + A2
C B – C A – A2 = B2 – 2 A B
A B + C B – C A – A2 = B2 – C B – A B
A B – C A – A2 = B2 – C B – A B
A ( B – C – A ) = B ( B – C – A )
A = B
1 = 1 – 0
1 ( 1 – 0 ) = ( 1 – 0 )2
1 ( 1 ) – 1 ( 0 ) = 12 – 2 ( 0 ) ( 1 ) + 02
1 ( 1 ) – 1 ( 0 ) – 02 = 12 – 2 ( 0 ) ( 1 )
0 ( 1 ) + 1 ( 1 ) – 1 ( 0 ) – 02 = 12 – 1 ( 1 ) – 0 ( 1 )
0 ( 1 ) – 1 ( 0 ) – 02 = 12 – 1 ( 1 ) – 0 ( 1 )
0 ( 1 – 1 – 0 ) = 1 ( 1 – 1 – 0 )
0 = 1
1 = 2 – 1
1 ( 2 – 1 ) = ( 2 – 1 )2
1 ( 2 ) – 1 ( 1 ) = 22 – 2 ( 1 ) ( 2 ) + 12
1 ( 2 ) – 1 ( 1 ) – 12 = 22 – 2 ( 1 ) ( 2 )
1 ( 2 ) + 1 ( 2 ) – 1 ( 1 ) – 12 = 22 – 1 ( 2 ) – 1 ( 2 )
1 ( 2 ) – 1 ( 1 ) – 12 = 22 – 1 ( 2 ) – 1 ( 2 )
1 ( 2 – 1 – 1 ) = 2 ( 2 – 1 – 1 )
1 = 2
1 = 3 – 2
1 ( 3 – 2 ) = ( 3 – 2 )2
1 ( 3 ) – 1 ( 2 ) = 32 – 2 ( 2 ) ( 3 ) + 22
1 ( 3 ) – 1 ( 2 ) – 22 = 32 – 2 ( 2 ) ( 3 )
2 ( 3 ) + 1 ( 3 ) – 1 ( 2 ) – 22 = 32 – 1 ( 3 ) – 2 ( 3 )
2 ( 3 ) – 1 ( 2 ) – 22 = 32 – 1 ( 3 ) – 2 ( 3 )
2 ( 3 – 1 – 2 ) = 3 ( 3 – 1 – 2 )
2 = 3
1 = 4 – 3
1 ( 4 – 3 ) = ( 4 – 3 )3
1 ( 4 ) – 1 ( 3 ) = 43 – 3 ( 3 ) ( 4 ) + 33
1 ( 4 ) – 1 ( 3 ) – 33 = 43 – 3 ( 3 ) ( 4 )
3 ( 4 ) + 1 ( 4 ) – 1 ( 3 ) – 33 = 43 – 1 ( 4 ) – 3 ( 4 )
3 ( 4 ) – 1 ( 3 ) – 33 = 43 – 1 ( 4 ) – 3 ( 4 )
3 ( 4 – 1 – 3 ) = 4 ( 4 – 1 – 3 )
3 = 4
1 = 5 – 4
1 ( 5 – 4 ) = ( 5 – 4 )2
1 ( 5 ) – 1 ( 4 ) = 52 – 2 ( 4 ) ( 5 ) + 42
1 ( 5 ) – 1 ( 4 ) – 42 = 52 – 2 ( 4 ) ( 5 )
4 ( 5 ) + 1 ( 5 ) – 1 ( 4 ) – 42 = 52 – 1 ( 5 ) – 4 ( 5 )
4 ( 5 ) – 1 ( 4 ) – 42 = 52 – 1 ( 5 ) – 4 ( 5 )
4 ( 5 – 1 – 4 ) = 5 ( 5 – 1 – 4 )
4 = 5
1 = 6 – 5
1 ( 6 – 5 ) = ( 6 – 5 )2
1 ( 6 ) – 1 ( 5 ) = 62 – 2 ( 5 ) ( 6 ) + 52
1 ( 6 ) – 1 ( 5 ) – 52 = 62 – 2 ( 5 ) ( 6 )
5 ( 6 ) + 1 ( 6 ) – 1 ( 5 ) – 52 = 62 – 1 ( 6 ) – 5 ( 6 )
5 ( 6 ) – 1 ( 5 ) – 52 = 62 – 1 ( 6 ) – 5 ( 6 )
5 ( 6 – 1 – 5 ) = 6 ( 6 – 1 – 5 )
5 = 6
1 = 7 – 6
1 ( 7 – 6 ) = ( 7 – 6 )2
1 ( 7 ) – 1 ( 6 ) = 72 – 2 ( 6 ) ( 7 ) + 62
1 ( 7 ) – 1 ( 6 ) – 62 = 72 – 2 ( 6 ) ( 7 )
6 ( 7 ) + 1 ( 7 ) – 1 ( 6 ) – 62 = 72 – 1 ( 7 ) – 6 ( 7 )
6 ( 7 ) – 1 ( 6 ) – 62 = 72 – 1 ( 7 ) – 6 ( 7 )
6 ( 7 – 1 – 6 ) = 7 ( 7 – 1 – 6 )
6 = 7
1 = 8 – 7
1 ( 8 – 7 ) = ( 8 – 7 )2
1 ( 8 ) – 1 ( 7 ) = 82 – 2 ( 7 ) ( 8 ) + 72
1 ( 8 ) – 1 ( 7 ) – 72 = 82 – 2 ( 7 ) ( 8 )
7 ( 8 ) + 1 ( 8 ) – 1 ( 7 ) – 72 = 82 – 1 ( 8 ) – 7 ( 8 )
7 ( 8 ) – 1 ( 7 ) – 72 = 82 – 1 ( 8 ) – 7 ( 8 )
7 ( 8 – 1 – 7 ) = 8 ( 8 – 1 – 7 )
7 = 8
1 = 9 – 8
1 ( 9 – 8 ) = ( 9 – 8 )2
1 ( 9 ) – 1 ( 8 ) = 92 – 2 ( 8 ) ( 9 ) + 82
1 ( 9 ) – 1 ( 8 ) – 82 = 92 – 2 ( 8 ) ( 9 )
8 ( 9 ) + 1 ( 9 ) – 1 ( 8 ) – 82 = 92 – 1 ( 9 ) – 8 ( 9 )
8 ( 9 ) – 1 ( 8 ) – 82 = 92 – 1 ( 9 ) – 8 ( 9 )
8 ( 9 – 1 – 8 ) = 9 ( 9 – 1 – 8 )
8 = 9
1 = 10 – 9
1 ( 10 – 9 ) = ( 10 – 9 )2
1 ( 10 ) – 1 ( 9 ) = 102 – 2 ( 9 ) ( 10 ) + 92
1 ( 10 ) – 1 ( 9 ) – 92 = 102 – 2 ( 9 ) ( 10 )
9 ( 10 ) + 1 ( 10 ) – 1 ( 9 ) – 92 = 102 – 1 ( 10 ) – 9 ( 10 )
9 ( 10 ) – 1 ( 9 ) – 92 = 102 – 1 ( 10 ) – 9 ( 10 )
9 ( 10 – 1 – 9 ) = 10 ( 10 – 1 – 9 )
9 = 10
Etc.
Using this logic, we can henceforth assume that all whole, rational numbers are equal to each other. Thusly, I have proven that math is completely useless to everyone.
>:3
End of Line.
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