sign
Let an agent treat sign as a well-defined property with conventions for zero and for signed zero in computing, rather than as a symbol only.
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 treat sign as a well-defined property with conventions for zero and for signed zero in computing, rather than as a symbol only.
In mathematics, the property of a nonzero real number of being positive or negative, and the symbol or function that expresses it.
What it is for: Expressing direction and polarity of quantities, and simplifying rules for arithmetic and comparison.
It can be determine it, with the sign function; change it, by negation; combine it, by the rules for multiplying signs; store it, as a sign bit in computer number formats.
Distinguishing features
Zero is neither positive nor negative in the usual convention
Floating point has a signed zero, with +0 and -0 compared equal but behaving differently
Sign generalises to complex numbers as x divided by its absolute value
Other senses of sign, such as signs and signage, are different entries
What it looks like
The symbols plus and minus, and the sign function sgn(x) that returns -1, 0 or 1.
How it is recognised
A leading minus or plus before a number
A sign bit in binary floating point or signed integer formats
The notation sgn(x) in formulas
Related models
is a property of - defined for nonzero reals
is related to - x equals sign times absolute value
is confused with - a homonym; this entry is mathematical
is represented by - how computers store it
In practice
Families and kinds
sign of a real number
sign function
sign bit in computer representations
sign of a permutation
Standards and regulation
IEEE 754 floating point, which defines signed zero and sign bit behaviour
ISO 80000-2 mathematical signs and symbols
Failure modes and hazards
Treating -0 and +0 as different in comparisons, or as the same where they differ
Losing the sign in conversions between formats
Integer overflow that flips the sign
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.sign-3
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 sign means for numbers.
Sign is simple for nonzero reals and conventional at zero and beyond the reals.
Real numbers
Positive, negative and zero.
Real sign
The sign of a real value and the rule for zero.
- What is the sign of this value, and which convention applies to zero? definition
- Is the value exactly zero or only rounded to zero? measurement
Extensions
Complex numbers and permutations.
Extended definitions
How sign is defined outside the reals.
- Which generalisation of sign applies here? definition
- Is the extension defined for this input? boundary
Arithmetic Rules for combining signs.
Sign rules drive simplification and error checking in calculations.
Sign rules
Products and quotients of signs.
Combination rules
The rules used.
- Which sign rules apply to this operation? definition
- Where do sign errors most often occur in this calculation? boundary
Comparison
Ordering by sign.
Ordering
How sign affects comparisons.
- How does sign affect ordering and comparison here? definition
- What happens with negative zero in comparisons? boundary
Computing Sign in number formats.
Computers store sign explicitly, and the representation leaks into results.
Representation
Sign bit, two complement.
Storage format
How sign is stored.
- How is sign represented in this number format? definition
- What range limits can flip the sign on overflow? boundary
Signed zero
Plus and minus zero.
Signed zero behaviour
Where signed zero changes results.
- Does signed zero change the result of this operation? boundary
- How should signed zero be displayed to people? action
Notation Writing sign.
Notation differs across typography and locales, and machine reading must handle the variants.
Symbols
Minus, hyphen and plus.
Symbol variants
The characters used.
- Which character represents the minus sign in this text? definition
- How should a hyphen used as minus be handled when parsing? action
Sign function
sgn(x) notation.
Function notation
How the sign function is written.
- Which notation for the sign function is used here? definition
- What value does it return at zero in this source? boundary
What the second pass must settle
- Should the sign of a permutation be a separate entry?
- How should the signed zero of floating point be modelled?
- Should the registry record which conventions an agent uses for sgn(0)?
- The registry entry has no aliases or definition; is the mathematical sense the one intended?