Real Numbers: Difference between revisions

Revision as of 16:20, 24 September 2025

Each number set contains the number set before it: $/ a$

N: Natural Numbers - ie all whole numbers.
- For example: 0,1,2... onwards
Z: Integers - ie all N plus negative integers.
- For example -2,-1,0,1,2...
D: Decimals - ie all Z plus fractions that can be written with a finite number of decimals.
- For example $11 / 4 = 2.75$
Q: Rationals - ie all D, plus those that do recur (but may never terminate.
- For example $1 / 3$ ( = 0.333333) or $143 / 999$ ( = 0.143143143)
R: Reals - ie all Q plus the irrationals, which are decimals that neither terminate nor recur.
- For example $π, \sqrt{2}, 3 \sqrt{3}, - \sqrt{2}, - \sqrt{5} / 2$ , etc

N is a subset of Z is a subset of D is a subset of Q is a subset of R

Intervals are ways of specifying the range of possible values for x:


Interval Type	Interval	Values for the real number x
Closed	$x \in [a, b] x \in [a, b [x \in] a, b] x \in] a, b [$	$a \leq x \leq b$ $a \leq x < b$ $a \leq x < b$ $a < x \leq b$ $a < x < b$
Open

@@ Line 24: / Line 24: @@
 |-
 |Closed
-|<math>x \in[a,b]</math>
+|<math>x \in[a,b]
+x \in[a,b[
-<math>x \in[a,b[</math>
+x \in]a,b]
-<math>x \in]a,b]</math>
+x \in]a,b[</math>
-<math>x \in]a,b[</math>
 |<math>a \leq x \leq b</math>
 <math>a \leq x < b</math>
@@ Line 49: / Line 48: @@
 |
 |}
 == Solving Inequalities ==