Exercises about Sets
... Write the sets with the roster method, set builder notation, and interval notation whenever possible. How many elements are in each set? Sketch the graph of each set on a Real number line. Use Venn diagrams to show the relationships between the sets involved in each question. a) N (2,5) b) N (-2 ...
... Write the sets with the roster method, set builder notation, and interval notation whenever possible. How many elements are in each set? Sketch the graph of each set on a Real number line. Use Venn diagrams to show the relationships between the sets involved in each question. a) N (2,5) b) N (-2 ...
Steps to adding and subtracting fractions
... 3. The LCM is 40, so the new denominators should be 40. 4. Find the new numerators: 2/5 = ?/40 (5 x 8 = 40, so multiply 2 x 8.) 2/5 = 16/40 3/8 = ?/40 (8 x 5 = 40, so multiply the 3 by 5.) 3/8 = 15/40 5. First, subtract the fractions: 16/40 – 15/40 = 1/40. 6. Next, subtract the whole numbers: 5 – 2 ...
... 3. The LCM is 40, so the new denominators should be 40. 4. Find the new numerators: 2/5 = ?/40 (5 x 8 = 40, so multiply 2 x 8.) 2/5 = 16/40 3/8 = ?/40 (8 x 5 = 40, so multiply the 3 by 5.) 3/8 = 15/40 5. First, subtract the fractions: 16/40 – 15/40 = 1/40. 6. Next, subtract the whole numbers: 5 – 2 ...
153 Problem Sheet 1
... (iii) Verify informally (so no rigorous proof is required) that a real number is rational if, and only if, its decimal expansion either terminates or repeats. (iv) Verify informally that if a and b are real numbers, with a < b then there exists a rational number c with a < c < b and there exists an ...
... (iii) Verify informally (so no rigorous proof is required) that a real number is rational if, and only if, its decimal expansion either terminates or repeats. (iv) Verify informally that if a and b are real numbers, with a < b then there exists a rational number c with a < c < b and there exists an ...
Example
... • Each point in the plane corresponds to an ordered pair (x, y) of real numbers. • The x and y values are called the coordinates of the point. • The coordinates for the origin are (0, 0). • The x-coordinate tells how many units the point is to the left or right of the origin. • If x is positive, th ...
... • Each point in the plane corresponds to an ordered pair (x, y) of real numbers. • The x and y values are called the coordinates of the point. • The coordinates for the origin are (0, 0). • The x-coordinate tells how many units the point is to the left or right of the origin. • If x is positive, th ...
Lecture 3. Mathematical Induction
... algorithms to recognize Mersenne primes and there are interesting ways to use them in number theory and algebra. It is not known yet whether there is an infinite number of Mersenne primes. Example 3 (Moser’s problem). The following problem arises in combinatorial geometry. Let S denote the unit circ ...
... algorithms to recognize Mersenne primes and there are interesting ways to use them in number theory and algebra. It is not known yet whether there is an infinite number of Mersenne primes. Example 3 (Moser’s problem). The following problem arises in combinatorial geometry. Let S denote the unit circ ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.