The real number line
A laboratory instrument never gives "the" exact value: it gives a range. Expressing that range unambiguously (as an interval, as a neighbourhood or as an inequality) is the language you will use constantly in physics, chemistry and technology.
Intervals and inequalities
Express as an interval and as an inequality the set of real numbers that are greater than or equal to $-3$ and strictly less than $5$.
Express as an interval and as an inequality the set of real numbers that are greater than or equal to $-3$ and strictly less than $5$.
Write as an interval the set of real numbers satisfying the condition $|x| \le 7$.
Write as an interval the set of real numbers satisfying the condition $|x| \le 7$.
Neighbourhoods: E(a, r)
Express the neighbourhood $E(-1, 3)$ as a numerical interval and describe it using an absolute value inequality.
Express the neighbourhood $E(-1, 3)$ as a numerical interval and describe it using an absolute value inequality.
Given the open interval $(2, 8)$, express it in neighbourhood notation, explicitly indicating its centre $a$ and its radius $r$.
Given the open interval $(2, 8)$, express it in neighbourhood notation, explicitly indicating its centre $a$ and its radius $r$.
Distance between two points on the line
Calculate the distance on the number line between points $A = -4,5$ and $B = 2,3$, and express the mathematical operation using absolute value notation.
Calculate the distance on the number line between points $A = -4,5$ and $B = 2,3$, and express the mathematical operation using absolute value notation.
State which of the following real numbers belong to the interval $[-1, \pi)$: $-1,01$, $-1$, $3,14$, $\frac{22}{7}$, $\sqrt{10}$.
State which of the following real numbers belong to the interval $[-1, \pi)$:
$-1,01$, $-1$, $3,14$, $\frac{22}{7}$, $\sqrt{10}$.
Operations with intervals: union, intersection, complement
Given the sets $A = (-\infty, 2]$, $B = (-1, 5)$ and $C = [0, +\infty)$, calculate $(A \cap B) \cup C$ and express the result as a single numerical interval.
Given the sets $A = (-\infty, 2]$, $B = (-1, 5)$ and $C = [0, +\infty)$, calculate $(A \cap B) \cup C$ and express the result as a single numerical interval.
Consider the interval $I = [-3, 4)$. Determine the complementary set $\mathbb{R} \setminus I$ and express it as the union of two intervals.
Consider the interval $I = [-3, 4)$. Determine the complementary set $\mathbb{R} \setminus I$ and express it as the union of two intervals.
Inequalities: from linear to quadratic
Solve the inequality $|2x - 5| \le 3$ and represent the solution set as an interval.
Solve the inequality $|2x - 5| \le 3$ and represent the solution set as an interval.
Express as a union of intervals the set of all real numbers satisfying the quadratic inequality $x^2 - 4x - 5 > 0$.
Express as a union of intervals the set of all real numbers satisfying the quadratic inequality $x^2 - 4x - 5 > 0$.
Back to the start: If a laboratory sensor measures $25{,}0\text{ ^\circ C}$ with an uncertainty of $0{,}2\text{ ^\circ C}$, its range is described with complete precision as the neighbourhood $E(25;\, 0{,}2)$, the inequality $|T - 25| < 0{,}2$ or the interval $(24{,}8;\, 25{,}2)$.