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Equation 19 · Part 6 · How Fast Can a Horizon Learn Which Path You Took?

subscript

Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}.T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}.
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

and a minimum-error decision time is Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}. Both are deterministic transformations of the assumed overlap law. Neither is a new field-theory result. Numerically inverting the two binary-entropy equations gives:

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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