From Newsgroup: sci.math

Am 08.05.2025 um 21:11 schrieb Python:

Le 08/05/2025 |a 20:32, Richard Hachel a |-crit:

A Cartesian coordinate system is a coordinate system used to locate
points in space using perpendicular lines called axes.

In a (2D) plane, a Cartesian coordinate system is generally composed of:

Two axes: the horizontal axis (called the x-axis), denoted by EYaN, and
the vertical axis (called the y-axis), denoted by EYaa.

An origin point, denoted by EYae, where the two axes intersect.

Identical units of measurement on each axis to allow for regular
reference points.

Each point on the plane can be represented by a pair of numbers (EYaN,EYaa),
called Cartesian coordinates.

These numbers indicate the position on the EYaN-axis and the EYaa-axis,
respectively.

A wide variety of mathematical elements can be plotted in a Cartesian
plane, including:
- Points. Each point is defined by its coordinates (x,y).
- Line segments and lines. A line segment connects two points. A line
can be drawn from an equation like y=2x+1.
- Curves (parabolas, circles, ellipses, hyperbolas, exponential
functions, sinusoidal functions, etc.).

When a line (such as a curve representing a function) crosses the x-
axis in a Cartesian coordinate system, this point of intersection is
called:
- a zero of the function
- a root of the function
- or a solution to the equation f(x)=0
These three terms are synonymous in this context.

Example: for the function f(x) = e^x - 1, we are looking for the value
for which f(x)=0.
Now, the curve f(x) intersects the x-axis at x=0. We say that x=0 is a
root (or zero) of the function.

R.H.

This is the worst definition one could propose.

Could you elaborate? (Ok, dual use of the terms "x" and "y" for
different purposes. But it's quite clear what is meant.)
--
Diese E-Mail wurde von Avast-Antivirussoftware auf Viren gepr|+ft. www.avast.com
--- Synchronet 3.21a-Linux NewsLink 1.2