nollställe

Nollställe is a Swedish term used in mathematics and measurement to denote a value at which a quantity becomes zero. In mathematics it most commonly refers to zeros or roots of a function, while in instrumentation it can refer to a reference point with zero value, such as a zero reference or ground.

In mathematics, a zero (nollställe) of a function f defined on a domain D is any x0 in D for which f(x0) = 0. The set of all zeros is often written as Z(f). For polynomials the zeros are the roots of the polynomial, and over the complex numbers a polynomial of degree n has exactly n roots counted with multiplicity (the Fundamental Theorem of Algebra). Real zeros may be fewer, and a real root can be simple (multiplicity 1) or multiple. Zeros can be found analytically, by factoring or applying formulas, or numerically through methods such as bisection or Newton-Raphson when a closed-form solution does not exist. Zeros of a function’s derivative correspond to stationary points, while zeros themselves are where the function crosses or touches the x-axis.

In measurement and engineering, nollställe can describe the zero reference level of a quantity. Instruments often include a zero-setting control to calibrate the display or output so that readings reflect deviations from a defined baseline, ensuring accurate interpretation of results.

Examples include f(x) = x^2 − 5, which has zeros at x = √5 and x = −√5, and sin(x), whose zeros occur at x = nπ for all integers n. The concept applies across disciplines wherever the idea of “being zero” is central to analysis or calibration.