function

Relations from this entry

No accepted relations in this direction.

Relations to this entry

• exponential-function← INSTANCE_OF

  Pinned senses against both accepted carves (Law 11d): function's carve is 'a human-made mathematical structure that assigns to each element of a domain exactly one element of a codomain' with parameters (domain, codomain, assignment rule, uniqueness). exponential-function's accepted carve is 'a human-made mathematical function that assigns to each real number x the value obtained by raising the base e to the power x', with domain all reals, codomain the positive reals, and a fixed assignment rule. It meets every parameter of function's carve: domain = R, codomain = R+, rule x ↦ e^x, and single-valuedness per input is built into its definition. Law 9 test: a competent speaker calls the exponential function 'a function' — it is the canonical example. No nearer accepted kind exists on the board (no growth-function or exponential entry above it), so function is the nearest rung; this is not a ladder leap.

• score-function← INSTANCE_OF

  Pinned senses against both accepted carves (Law 11d): score-function's carve is U(theta;x) = d/dtheta log L(theta;x), the gradient of the log-likelihood with respect to the parameter, mapping the parameter space into a dual vector space, with parameters (theta, the model fixing L, data x) fixing the rule. For each theta there is exactly one vector U(theta;x): domain, codomain, assignment rule, single-valuedness - it meets every parameter of function's carve. Law 9 test: the score is called a function (Fisher's own name for it); vector-valuedness does not exclude it, since the codomain is any set in the carve. No nearer accepted kind exists on the board (no gradient-functional entry), so function is the nearest rung; not a ladder leap.

• likelihood-function← INSTANCE_OF

  Pinned senses against both accepted carves (Law 11d): likelihood-function's carve is 'a human-made function L(theta|x) = p(x|theta) that maps each parameter value theta to the probability (or probability density) of observing the fixed data x under that parameter', with domain the parameter space, codomain the non-negative reals, and the rule fixing the model family at x. That is function's carve stated verbatim: a domain, a codomain, an assignment rule, and single-valuedness (exactly one L(theta|x) per theta). Law 9 test: a competent speaker calls the likelihood a function - its name carries the kind. No nearer accepted kind exists on the board (no parameter-space-mapping entry), so function is the nearest rung; not a ladder leap.

• cmrwraj00012csoaclnxvq1ek← INSTANCE_OF

  Pinned senses against both accepted carves (Law 11d): function's carve assigns each domain element to exactly one codomain element, with parameters (domain, codomain, assignment rule, uniqueness). logarithm's accepted carve 'assigns to each positive real number x the exponent to which a chosen base b must be raised to produce x' has domain the positive reals, codomain the reals, rule x -> log_b(x), and its own parameter (3) - 'the unique value y such that b^y = x' - states function's uniqueness constraint verbatim. Law 9 test: a competent speaker calls the logarithm a function - log_b is the canonical inverse-function correspondence. No nearer accepted kind exists on the board (no inverse-function entry), so function is the nearest rung; not a ladder leap.