En esta entrada vamos a tratar los números reales y los intervalos en inglés.
Real Numbers
Natural Numbers:
ℕ={1,2 ,3, 4,5, 6,…}
Natural numbers can be used for counting
Integers
ℤ={… ,−3,−2,−1,0,1,2,3 ,…}
The set of integers is formed by the natural numbers including zero and the negatives, the opposites of the natural numbers.
Rational Numbers:
ℚ={a/b, where a, b∈ℤ , b≠0}
Rational numbers are the fractions. All number that can be written as a fraction is a rational number.
Irrational Numbers
ℝ-ℚ. Irrational numbers have an infinite number of digits to the right of the decimal point, without repetition.
Examples: π; ; 1.2432568456…
Real Numbers
ℝ=ℚ∪(ℝ-ℚ)
The real numbers include rational numbers and irrational numbers.
Intervals
A real interval is a subset of real numbers that corresponds to the points of a segment or a half-line on the real line.
| INTERVAL NOTATION | SET NOTATION | GEOMETRIC PICTURE |
| (a,b) | {x∈ℝ:a<x<b} | |
Exercises about real numbers
- Classify the following numbers into the corresponding set:
| 3/2 | |||||||||
| Natural Numbers ℕ |
|||||||||
| Integers ℤ | |||||||||
| Rational Numbers ℚ |
|||||||||
| Irrational Numbers ℝ-ℚ |
|||||||||
| Real Numbers ℝ |
2. Calculate the diagonal of a square whose side is 1 cm long.
3. Which of the following numbers are rational?
a) 1,434343… b) 1,432432243222… c) 1,4232323…
d) 1,22222… e) 1,1254326784… f) 0,12
4. Complete the table
| INTERVAL NOTATION | SET NOTATION | GEOMETRIC PICTURE |
| {x∈ℝ:-2<x<6} | ||
 |
||
| (-∞,3] |
5. Write as intervals and represent on the real line the following set of numbers:
a) Greatest than -3 and less than 3
b) Greatest or equal than 2.
c) Less than 2.
d) Less or equal than -1.
e) Greatest than -1.
f) Greatest or equal than -2 and less than 3.
