NROCDavidsUnit2
... Many problems in mathematics deal with whole numbers, which are used to count whole units of things. For example, you can count students in a classroom and the number of dollar bills. You need other kinds of numbers to describe units that are not whole. For example, an aquarium might be partly full. ...
... Many problems in mathematics deal with whole numbers, which are used to count whole units of things. For example, you can count students in a classroom and the number of dollar bills. You need other kinds of numbers to describe units that are not whole. For example, an aquarium might be partly full. ...
Equivalence Relations
... The concept of equivalence relation is an abstraction of the idea of two math objects being like each other in some respect. If an object a is like an object b in some specified way, then b is like a in that respect. a is like itself in every respect! So if you want to give an abstract definitio ...
... The concept of equivalence relation is an abstraction of the idea of two math objects being like each other in some respect. If an object a is like an object b in some specified way, then b is like a in that respect. a is like itself in every respect! So if you want to give an abstract definitio ...
FERMAT’S TEST 1. Introduction
... √ Let n = 415693, as in the previous example. While n has only one nontrivial factor below n, the number of a from 1 to n − 1 such that (a, n) > 1 is 1293, so there is a better chance of randomly picking an integer less than n that shares √ a common nontrivial factor with n than there is of picking ...
... √ Let n = 415693, as in the previous example. While n has only one nontrivial factor below n, the number of a from 1 to n − 1 such that (a, n) > 1 is 1293, so there is a better chance of randomly picking an integer less than n that shares √ a common nontrivial factor with n than there is of picking ...
I. Sequence
... B. Theorem 6 – The Nondecreasing Sequence Thm A nondecreasing sequence of real numbers converges iff it is bounded from above. If a nondecreasing sequence converges, it converges to its least upper bound. Thm 6 implies that a nondecreasing sequence converges when it is bounded from above. It diverg ...
... B. Theorem 6 – The Nondecreasing Sequence Thm A nondecreasing sequence of real numbers converges iff it is bounded from above. If a nondecreasing sequence converges, it converges to its least upper bound. Thm 6 implies that a nondecreasing sequence converges when it is bounded from above. It diverg ...
PRIMITIVE PYTHAGOREAN TRIPLES WITH SUM OR DIFFERENCE
... triple according to (1.1). In this paper I will adhere to the following conventions: (a) The first entry of a pythagorean triple will be the even leg of the triple. (b) The second entry of a pythagorean triple will be the odd leg of the triple. (c) The third entry of a pythagorean triple will be the ...
... triple according to (1.1). In this paper I will adhere to the following conventions: (a) The first entry of a pythagorean triple will be the even leg of the triple. (b) The second entry of a pythagorean triple will be the odd leg of the triple. (c) The third entry of a pythagorean triple will be the ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.