Situation 39: Summing Natural Numbers
... particular kind that facilitate finding a sum; under any such rearrangement of the elements of a discrete set, the cardinality remains the same, as does the sum of the elements. A formula for the sum of the natural numbers from 1 to any number can be developed from, and verified for, specific instan ...
... particular kind that facilitate finding a sum; under any such rearrangement of the elements of a discrete set, the cardinality remains the same, as does the sum of the elements. A formula for the sum of the natural numbers from 1 to any number can be developed from, and verified for, specific instan ...
Guide to written methods for subtraction
... and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher. ...
... and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher. ...
INTEGERS
... Tip: It may help to think of positive numbers as a GAIN and negative numbers as a LOSS when adding integers. When you add two positive integers or gains, you have a bigger gain so the result is still positive. When you add two negative integers or losses, you have a bigger loss so the result remains ...
... Tip: It may help to think of positive numbers as a GAIN and negative numbers as a LOSS when adding integers. When you add two positive integers or gains, you have a bigger gain so the result is still positive. When you add two negative integers or losses, you have a bigger loss so the result remains ...
Full text
... segment intersects the x-axis. A line segment that does not intersect the x-axis will only change its slope and length but not be folded. These are useful in graphical analysis of iterates. For ju in the range 0< // < 1, the T^ map is simple, as there is one stable fixed point x* = 1/(1 + //), and t ...
... segment intersects the x-axis. A line segment that does not intersect the x-axis will only change its slope and length but not be folded. These are useful in graphical analysis of iterates. For ju in the range 0< // < 1, the T^ map is simple, as there is one stable fixed point x* = 1/(1 + //), and t ...
N1 Integers - Haringeymath's Blog
... If a whole number has two, and only two, factors it is called a prime number. For example, the number 17 has only two factors, 1 and 17. Therefore, 17 is a prime number. The number 1 has only one factor, 1. Therefore, 1 is not a prime number. ...
... If a whole number has two, and only two, factors it is called a prime number. For example, the number 17 has only two factors, 1 and 17. Therefore, 17 is a prime number. The number 1 has only one factor, 1. Therefore, 1 is not a prime number. ...
Sequences and Series
... A finite sequence is a function whose domain is the set of positive integers less than or equal to some fixed positive integer. An infinite sequence is a function whose domain is the set of all positive integers. When the domain is apparent, we will refer to either a finite sequence or an infinite s ...
... A finite sequence is a function whose domain is the set of positive integers less than or equal to some fixed positive integer. An infinite sequence is a function whose domain is the set of all positive integers. When the domain is apparent, we will refer to either a finite sequence or an infinite s ...
1-5 Roots and Irrational Numbers
... • A repeating decimal has a block of one or more digits after the decimal point that repeat continuously (where all digits are not zeros). ...
... • A repeating decimal has a block of one or more digits after the decimal point that repeat continuously (where all digits are not zeros). ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.