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Equation 20 · Part 2 · The Economics and Physical Limits of Running AI Agents at Scale

subtraction

n(n−1)/2n(n-1)/2
subtraction

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

The middle term is the one that matters. It grows as n(n-1)/2 — quadratically in step count — while the other two terms grow only linearly. For a short loop, the quadratic term is negligible next to the fixed tax and the output cost. For a long one, it dominates completely, and no amount of shrinking τ\tau or oˉ\bar{o} changes that; the loop’s own length has become the largest line item, all by itself.

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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