Symbol in context

$u$

This entry links every published equation using this exact notation. Its meaning may change between equations.

Meanings in context

Article-grounded definition

Symbol u

the unit roundoff — roughly 10^{-16} for standard double precision — and $\mathrm{op}$ is addition, subtraction, multiplication, or division.

Read equation 1 in How Mathematics, Proof, and Scientific Computation Actually Work →

Article-grounded definition

Symbol u

the rounding error governed by machine precision.

Read equation 1 in Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation →

Article-grounded definition

Symbol u

required human or institutional authorization.

Read equation 42 in OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence →

Used in 23 equations

h_v^{(k+1)} = \phi\left(h_v^{(k)}, \bigoplus_{u \in \mathcal{N}(v)} \psi\left(h_v^{(k)}, h_u^{(k)}, e_{uv}\right)\right),

How AI for Science and Medicine Actually Works · Equation 9

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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u

How AI for Science and Medicine Actually Works · Equation 14

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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u \in (0, 1]

Comparing the Main Approaches to AI Inference Economics · Equation 9

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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P_r < u \cdot P_d, \qquad \text{i.e.} \qquad u > \frac{P_r}{P_d} \equiv u^{*}.

Comparing the Main Approaches to AI Inference Economics · Equation 10

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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u

Comparing the Main Approaches to AI Inference Economics · Equation 12

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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u\in\mathcal A(t_c)

How Fast Can a Horizon Learn Which Path You Took? · Equation 39

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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D_{\rm irr}(t_c)= \inf_{u\in\mathcal A(t_c)} \frac12\left\|\rho^{u}_{0,H}-\rho^{u}_{1,H}\right\|_1.

How Fast Can a Horizon Learn Which Path You Took? · Equation 42

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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u_c^2(y) = \sum_{i=1}^{N} \left(\frac{\partial f}{\partial x_i}\right)^2 u^2(x_i) \;+\; 2\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} \frac{\partial f}{\partial x_i}\frac{\partial f}{\partial x_j}\, u(x_i, x_j)

How Scientific Instruments and Metrology Actually Work · Equation 4

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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\mathrm{fl}(x \mathbin{\text{op}} y) = (x \mathbin{\text{op}} y)(1 + \delta), \qquad |\delta| \le u,

How Mathematics, Proof, and Scientific Computation Actually Work · Equation 1

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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u

How Mathematics, Proof, and Scientific Computation Actually Work · Equation 2

the unit roundoff — roughly 10^{-16} for standard double precision — and $\mathrm{op}$ is addition, subtraction, multiplication, or division.

Equation guide → · This term → · Article →

u

How Mathematics, Proof, and Scientific Computation Actually Work · Equation 5

the unit roundoff — roughly 10^{-16} for standard double precision — and $\mathrm{op}$ is addition, subtraction, multiplication, or division.

Equation guide → · This term → · Article →

\hat{f}(x) = f(x) + \varepsilon_{\text{disc}}(h) + \varepsilon_{\text{round}}(u) + \varepsilon_{\text{model}}

Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation · Equation 1

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Equation guide → · This term → · Article →

u

Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation · Equation 4

the rounding error governed by machine precision.

Equation guide → · This term → · Article →

u(p,t)

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 17

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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u(0,t)=0

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 18

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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u(1,t)=1

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 19

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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u(p) = \frac{1-e^{-4Nsp}}{1-e^{-4Ns}}

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 28

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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u(p) = p \qquad (s \to 0).

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 29

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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u

The Hardest Unsolved Problems in Meta, Llama, and Open-Weight AI · Equation 1

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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L(u) = \begin{cases} 1, & u \le 7 \times 10^{8} \\ g, & u > 7 \times 10^{8} \end{cases}

The Hardest Unsolved Problems in Meta, Llama, and Open-Weight AI · Equation 2

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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\operatorname{sim}(u, v) = \frac{\langle u, v \rangle}{\lVert u \rVert \, \lVert v \rVert}.

Embeddings and the Geometry of Similarity · Equation 1

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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\operatorname{accept}(s') = \mathbb{1}\!\left[ \bigwedge_{i=1}^{m} v_i(s')=1 \right] \cdot u(s'),

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 42

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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u(s')

OpenAI Codex as a Software-Engineering System: Models, Harnesses, and Evidence · Equation 43

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

uuu

Meanings in context

Symbol u

Symbol u

Symbol u

Used in 23 equations

$u$