Interval Notation and Real Numbers

The video tutorial introduces interval notation, a method for representing intervals on the real number line. It compares set-builder notation with interval notation, explaining the use of open and closed intervals. The tutorial also covers infinite intervals and the union of sets, providing a comprehensive understanding of how to represent intervals in mathematics.

What is the primary purpose of interval notation?

• To represent complex numbers

• To solve algebraic equations

• To represent intervals of real numbers

• To graph functions

Which of the following is NOT a feature of the real number line?

• It includes all real numbers

• It can represent complex numbers

• It can be divided into intervals

• It extends infinitely in both directions

How can the set of all real numbers from 0 to 2, including 0 and 2, be represented using set-builder notation?

• {x | 0 ≤ x < 2}

• {x | 0 < x ≤ 2}

• {x | 0 ≤ x ≤ 2}

• {x | 0 < x < 2}

What do square brackets in interval notation indicate?

• The interval is infinite

• The interval is closed

• The interval is undefined

• The interval is open

How is an open interval from 0 to 2 represented in interval notation?

• [0, 2]

• (0, 2)

• (0, 2]

• [0, 2)

What change is made to interval notation to represent a half-open interval from 0 to 2, including 2?

• Use a square bracket on the left and a parenthesis on the right

• Use a square bracket on the right and a parenthesis on the left

• Use parentheses on both sides

• Use square brackets on both sides

How is the interval from negative infinity to zero represented in interval notation?

• (-∞, 0]

• (-∞, 0)

• [0, ∞)

• (0, ∞)

What does the union symbol in interval notation signify?

• Intersection of intervals

• Difference of intervals

• Symmetric difference of intervals

• Combination of intervals

Which of the following is true about intervals involving infinity?

• They cannot be represented

• They must use parentheses

• They must use square brackets

• They can include infinity

What is the interval notation for all real numbers?

• [0, ∞)

• (-∞, 0]

• [0, 1]

• (-∞, ∞)