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Pascal's triangle
With Pascal's triangle you can show that (1 + 1)0 = 20 = 1.
Explanation
If you write the binomial theorem (a + b)n as (1 + 1)n all a's and b's in the expansion are omitted, and only the binomial coefficients remain. The sum of each row are powers of two, because (1 + 1)n = 2n.
0 1 → 1 = 20 1 1 1 → 2 = 21 2 1 2 1 → 4 = 22 3 1 3 3 1 → 8 = 23 4 1 4 6 4 1 → 16 = 24 5 1 5 10 10 5 1 → 32 = 25 6 1 6 15 20 15 6 1 → 64 = 26 7 1 7 21 35 35 21 7 1 → 128 = 27
In row three you get 23 = 1 + 3 + 3 + 1 = 8. For row zero it gives 20 = 1.