That's a huge board

The numbers 1000, 1001, ..., 2999 have been written on a board. Each time, one is allowed to erase two numbers, say $$a$$ and $$b$$, and replace by the number $$\frac {1}{2} \min(a, b)$$.

After 1999 such operations, one obtains exactly one number $$c$$ on the board. Prove that $$c < 1$$.

Note by Sharky Kesa
4 years, 1 month ago

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