Equation 3 · Part 1 · How Mathematics, Proof, and Scientific Computation Actually Work
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
where u is the unit roundoff — roughly 10^{-16} for standard double precision — and is addition, subtraction, multiplication, or division. Each single step, in other words, is correct up to a tiny, precisely bounded relative error.
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Open the illustrated exponents: repeated multiplication and powers guide →
Sources cited in the article section
- [5] IEEE 754-2019 — IEEE Standard for Floating-Point Arithmetic ↗
- [6] Accuracy and Stability of Numerical Algorithms (2nd ed.) ↗
These citations provide research context; check each source for the exact claim it supports.