Chapter 1
... 2.1.4.1.4. There are just as many elements in W as there are in N, O, or E 2.1.4.2. Finding all the subsets of a finite set of whole numbers 2.1.4.2.1. See example 2.5 p. 62 2.1.4.2.2. Your turn p. 63: Do the practice and the reflect 2.1.4.2.3. Mini-investigation 2.4 – Finding a pattern 2.1.5. Three ...
... 2.1.4.1.4. There are just as many elements in W as there are in N, O, or E 2.1.4.2. Finding all the subsets of a finite set of whole numbers 2.1.4.2.1. See example 2.5 p. 62 2.1.4.2.2. Your turn p. 63: Do the practice and the reflect 2.1.4.2.3. Mini-investigation 2.4 – Finding a pattern 2.1.5. Three ...
Document
... Read the mathematical definition in the left column and the sentence in the right column. In the blank in the middle, write the one word from the list below that fits both the definition and the sentence. The first one is done for you. base natural real ...
... Read the mathematical definition in the left column and the sentence in the right column. In the blank in the middle, write the one word from the list below that fits both the definition and the sentence. The first one is done for you. base natural real ...
Chapter 02 – Section 01
... For example, if you are playing tug-of-war and one side pulls with a force of 100 Newtons (metric unit of force) and the other side also pulls with 100 Newtons of force, how can you describe the fact that neither side is winning the pull? Both pull with equal strength, just in opposite directions. T ...
... For example, if you are playing tug-of-war and one side pulls with a force of 100 Newtons (metric unit of force) and the other side also pulls with 100 Newtons of force, how can you describe the fact that neither side is winning the pull? Both pull with equal strength, just in opposite directions. T ...
EXPLORING INTEGERS ON THE NUMBER LINE
... 1. The post office is located at the origin of Main Street. We label its address as 0. The laboratory has address 6 and the zoo has address 9. Going in the other direction from the origin, we find a candy shop with address –4 and a space observatory with address –7. Draw a number line representing ...
... 1. The post office is located at the origin of Main Street. We label its address as 0. The laboratory has address 6 and the zoo has address 9. Going in the other direction from the origin, we find a candy shop with address –4 and a space observatory with address –7. Draw a number line representing ...
m120cn3
... Addition of Whole Numbers The concept of whole number addition can be described (or defined) in terms of sets. If a set A contains a elements and a set B contains b elements, and AB=Ø, then a+b is the number of elements in AB. In the equation a+b=c, a and b are called the addends and c is called ...
... Addition of Whole Numbers The concept of whole number addition can be described (or defined) in terms of sets. If a set A contains a elements and a set B contains b elements, and AB=Ø, then a+b is the number of elements in AB. In the equation a+b=c, a and b are called the addends and c is called ...
Document
... And one last set of numbers (the big one…): • Real numbers – the set of all rational and irrational numbers combined Comments about the real numbers: • When you draw a number line, every point on the line is associated with a real number – the number tells how far the point is from zero, the middle ...
... And one last set of numbers (the big one…): • Real numbers – the set of all rational and irrational numbers combined Comments about the real numbers: • When you draw a number line, every point on the line is associated with a real number – the number tells how far the point is from zero, the middle ...
a < b
... A combination of variables and numbers using the operations of addition, subtraction, multiplication, or division, as well as powers or roots, is called an algebraic expression. Note: there is NO EQUAL SIGN, and we can only SIMPLIFY, not SOLVE! Here are some examples of algebraic expressions: ...
... A combination of variables and numbers using the operations of addition, subtraction, multiplication, or division, as well as powers or roots, is called an algebraic expression. Note: there is NO EQUAL SIGN, and we can only SIMPLIFY, not SOLVE! Here are some examples of algebraic expressions: ...
Readings for Lecture/Lab 1 – Sets and Whole Numbers How are the
... How many other distinct one-to-one correspondences could be made where a, b, c are kept in the same order? What are they? That is, how many different one-to-one correspondences could be made? Important Note. Equal sets are equivalent, but equivalent sets may not be equal. This was illustrated in the ...
... How many other distinct one-to-one correspondences could be made where a, b, c are kept in the same order? What are they? That is, how many different one-to-one correspondences could be made? Important Note. Equal sets are equivalent, but equivalent sets may not be equal. This was illustrated in the ...
MRWC Notes 2.A
... model rational numbers graphically, and give rational representations of numbers. ...
... model rational numbers graphically, and give rational representations of numbers. ...
Unit 1 - Review of Real Number System
... Like signs: to add two numbers with the same sign, add their absolute values. The sign of the answer is the same as the sign of the two numbers. Unlike signs: subtract the smaller absolute value from the larger. The sign of the answer is the same as the number with the largest absolute value. Subtra ...
... Like signs: to add two numbers with the same sign, add their absolute values. The sign of the answer is the same as the sign of the two numbers. Unlike signs: subtract the smaller absolute value from the larger. The sign of the answer is the same as the number with the largest absolute value. Subtra ...
Surreal number
In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. (Strictly speaking, the surreals are not a set, but a proper class.) If formulated in Von Neumann–Bernays–Gödel set theory, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, can be realized as subfields of the surreals. It has also been shown (in Von Neumann–Bernays–Gödel set theory) that the maximal class hyperreal field is isomorphic to the maximal class surreal field; in theories without the axiom of global choice, this need not be the case, and in such theories it is not necessarily true that the surreals are the largest ordered field. The surreals also contain all transfinite ordinal numbers; the arithmetic on them is given by the natural operations.In 1907 Hahn introduced Hahn series as a generalization of formal power series, and Hausdorff introduced certain ordered sets called ηα-sets for ordinals α and asked if it was possible to find a compatible ordered group or field structure. In 1962 Alling used a modified form of Hahn series to construct such ordered fields associated to certain ordinals α, and taking α to be the class of all ordinals in his construction gives a class that is an ordered field isomorphic to the surreal numbers.Research on the go endgame by John Horton Conway led to a simpler definition and construction of the surreal numbers. Conway's construction was introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. In his book, which takes the form of a dialogue, Knuth coined the term surreal numbers for what Conway had called simply numbers. Conway later adopted Knuth's term, and used surreals for analyzing games in his 1976 book On Numbers and Games.