1-3 Integers and Absolute Value
... 1-3 Integers and Absolute Value Additional Example 1B: Sports Application Use <, >, or = to compare the scores. List the golf scores in order from the lowest to the highest. The scores are –4, 2, 5, and –3. Place the scores on the number line and read them from left to right. ...
... 1-3 Integers and Absolute Value Additional Example 1B: Sports Application Use <, >, or = to compare the scores. List the golf scores in order from the lowest to the highest. The scores are –4, 2, 5, and –3. Place the scores on the number line and read them from left to right. ...
A , B
... A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s ...
... A good example that you can “relate” to is students in our maths class this semester are set A. The grade they earn out of the class is set B. Each student must be assigned a grade and can only be assigned ONE grade, but more than one student can get the same grade (we hope so---we want lots of A’s ...
generalized cantor expansions 3rd edition - Rose
... numbers from their representations. In this paper, we will examine the various types of representations for numbers. The simplest and most familiar is base-10, which is commonly used in everyday life. However a more uncommon way to represent a number is the so called cantor expansion of the number. ...
... numbers from their representations. In this paper, we will examine the various types of representations for numbers. The simplest and most familiar is base-10, which is commonly used in everyday life. However a more uncommon way to represent a number is the so called cantor expansion of the number. ...
Set-Builder Notation
... • Set-Builder Notation: describes, but does not explicitly list the elements of a set. • Example: {x | x is an even number}, – The | (vertical bar) is pronounced “such that” ...
... • Set-Builder Notation: describes, but does not explicitly list the elements of a set. • Example: {x | x is an even number}, – The | (vertical bar) is pronounced “such that” ...
Remainder Theorem
... Factor Theorem If the remainder f(r) = R = 0, then (x-r) is a factor of f(x). The Factor Theorem is powerful because it can be used to find the roots of polynomial equations. Example 3: Is x 4 a factor of 3x 3 x 2 20 x 5 ? For this question we need to find out if dividing 3x 3 x 2 20 x ...
... Factor Theorem If the remainder f(r) = R = 0, then (x-r) is a factor of f(x). The Factor Theorem is powerful because it can be used to find the roots of polynomial equations. Example 3: Is x 4 a factor of 3x 3 x 2 20 x 5 ? For this question we need to find out if dividing 3x 3 x 2 20 x ...
Collatz Function like Integral Value Transformations
... problems is Collatz Conjecture [1, 2] in number theory and discrete dynamical systems proposed by L. Collatz in 1937. Although the problem on which the conjecture is built is remarkably simple to explain and understand, the nature of the conjecture and the behavior of this dynamical system for provi ...
... problems is Collatz Conjecture [1, 2] in number theory and discrete dynamical systems proposed by L. Collatz in 1937. Although the problem on which the conjecture is built is remarkably simple to explain and understand, the nature of the conjecture and the behavior of this dynamical system for provi ...
Arithmetic Sequences
... value of the common ratio is strictly less than one. (This ensures that the absolute value of each subsequent term is decreasing, whereas no such guarantee can be made about an arithmetic sequence of any sort. Note however that this observation does NOT guarantee a convergent sum.) Imagine the same ...
... value of the common ratio is strictly less than one. (This ensures that the absolute value of each subsequent term is decreasing, whereas no such guarantee can be made about an arithmetic sequence of any sort. Note however that this observation does NOT guarantee a convergent sum.) Imagine the same ...
UNIT 3: Divisibility in Natural Numbers 3.1 Relationship of divisibility
... Method 2 To work out the H.C.F. of several numbers, first write them as a product of their primes factors and then take only the common factors with the least exponent Example: Find the H.C.F of 40 and 60 ...
... Method 2 To work out the H.C.F. of several numbers, first write them as a product of their primes factors and then take only the common factors with the least exponent Example: Find the H.C.F of 40 and 60 ...
Solving Equations Finding the value of a variable
... (two basic problems in one) Simplify anything that can be simplified. ? Any like terms on the same side of the equal sign? ...
... (two basic problems in one) Simplify anything that can be simplified. ? Any like terms on the same side of the equal sign? ...
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)