26 December 2021 Interval notation LO To understand

26 December 2021 Interval notation LO: To understand use interval notation for subsets of the Real numbers. www. mathssupport. org

Interval notation A shorthand used to write sets, often sets with an infinite number of elements. For interval notation we use curly brackets { }, variables and other symbols to express the set. The set of Less than or equal to Greater than or equal to Is a member of the set of real numbers Union (or) Such that www. mathssupport. org {} < ≤ > ℝ |

Interval Notation For example: Graphically a b a a a b b Interval notation Set notation x<a {x|x < a, x ∊ ℝ} a<x<b {x|a < x < b, x ∊ ℝ} x < a or x > b {x| x < a or x > b, x ∊ ℝ} a<x b {x|a < x b, x ∊ ℝ} The filled in circle indicates the inclusion of the end point The open circle indicates the non-inclusion of the end point www. mathssupport. org

Interval Notation If the interval goes forever to the left, the set goes to -∞. For example, The interval is the set of numbers that are all less than 3, including 3. Graphically -∞ 3 You can write using interval notation x 3 You can write using set notation {x|x 3, x ∊ ℝ} www. mathssupport. org

Interval Notation If the interval goes forever to the right, the set goes to ∞. For example, The interval is the set of numbers that are all greater than -5. Graphically -∞ – 5 ∞ You can write using interval notation x – 5 You can write using set notation {x|x > – 5, x ∊ ℝ} www. mathssupport. org

Interval Notation If the interval includes the boundaries, is represented by filled in circles. For example, The interval is the set of numbers that are all greater than -3 but less than 2, including -3 and 2. Graphically -3 2 You can write using interval notation -3 ≤ x ≤ 2 You can write using set notation {x|-3 ≤ x ≤ 2, x ∊ ℝ} www. mathssupport. org

Interval Notation If the interval does not include the boundaries, is represented by empty circles. For example, The interval is the set of numbers that are all greater than 4 but less than 10. Graphically 4 10 You can write using interval notation 4 < x < 10 You can write using set notation {x|4 < x < 10, x ∊ ℝ} www. mathssupport. org

Interval Notation If the interval is from the set of Integers, it is not an infinite set For example, The interval is the set of numbers that are all greater than 3 but less than 7 and are all integers. Graphically 2 3 4 5 6 7 8 You can write the list of elements {4, 5, 6} You can write using set notation {x|3 < x < 7, x ∊ ℤ} www. mathssupport. org

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