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Research draft

absolute value

vr.tr.absolute-value · XCT.QTY

Let an agent handle absolute value by definition, properties, generalisations and applications.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent handle absolute value by definition, properties, generalisations and applications.

The non-negative magnitude of a real number without regard to its sign, written |x|; generalised to the modulus of a complex number and the length (norm) of a vector.

What it is for: Measuring size and distance regardless of direction.

It can be compute absolute values; solve absolute value equations; compute absolute differences; generalise to norms.

Distinguishing features

Non-negative

Distance from zero

Even, piecewise function

Triangle inequality holds

What it looks like

Vertical bars around a quantity.

How it is recognised

Notation |x|

V-shaped graph

Modulus of complex numbers

Related models

is a kind of - category

function

generalises to - concept

norm

is related to - modulus

complex number

measures - meaning

distance

In practice

Families and kinds

absolute value of real numbers

modulus of complex numbers

vector norms

absolute difference

Standards and regulation

ISO 80000-2 notation

Failure modes and hazards

Dropping cases when solving equations

Confusing with brackets in notation

Also called

vector lengthprice base amountabsolute difference

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Also registered as vr.tr.absolute-value

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Definition What it is.

Definition is simple.

Compute

Value.

Compute

Computation.

  1. What is the absolute value of this number? measurement
  2. What is the absolute difference between two values? measurement

Graph

Shape.

Graph

Graph.

  1. What does the graph look like? definition
  2. Where is it not differentiable? definition
Properties Rules.

Properties help proofs.

Triangle inequality

Bound.

Triangle

Triangle inequality.

  1. How does the triangle inequality apply? definition
  2. What other properties hold? definition

Equations

Solving.

Equations

Absolute value equations.

  1. Which cases must be considered when solving? action
  2. Are all solutions checked? boundary
Generalisation Complex and vectors.

The idea extends.

Complex

Modulus.

Complex

Modulus.

  1. What is the modulus of this complex number? measurement
  2. How is it computed? definition

Norm

Vectors.

Norm

Vector norm.

  1. Which norm is used for vector length? definition
  2. What is its value? measurement
Use Applications.

Absolute value is common.

Errors

Absolute error.

Errors

Absolute error.

  1. What is the absolute error of this measurement? measurement
  2. How does it differ from relative error? definition

Computing

Functions.

Computing

Computing.

  1. How is absolute value computed in code? action
  2. What happens at the minimum integer value? boundary

What the second pass must settle

  • Should norms be a separate entry?
  • How should notation be linked?
  • How should the economic sense be split off?
Draft as JSON