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Equation 1 · Part 6 · A Timeline of xAI, Grok, and Colossus

Denominator: 92

r=100,00092≈1,087 GPUs installed per day.r = \frac{100{,}000}{92} \approx 1{,}087 \text{ GPUs installed per day.}
9292

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

92 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

xAI announced a doubling of the original cluster to 200,000 GPUs within roughly ninety days of the initial buildout, adding Nvidia H200s alongside the original H100s [ 16 ] . That kind of headline — “doubled in ninety-two days” — is easy to read two different ways, and the difference matters for judging how the next expansion phase should be interpreted. Read as a constant installation rate, doubling 100,000 GPUs to 200,000 over ninety-two days implies roughly r=100,00092≈1,087 GPUs installed per day.r = \frac{100{,}000}{92} \approx 1{,}087 \text{ GPUs installed per day.}. Read instead as a constant compounding rate — the assumption implicit whenever a “doubled again” claim is extrapolated forward — the same ninety-two-day doubling implies a daily multiplicative growth rate g solving…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.