Class : IX Holiday-Home work (2015-16)
... 1. Write one rational number between 3 and 4. 2. Justify 2.010010001…..is an irrational number. 3. Am I right if I say only 100 rational numbers can be inserted between 1 and 101? 4. Every Rational number is .. ...
... 1. Write one rational number between 3 and 4. 2. Justify 2.010010001…..is an irrational number. 3. Am I right if I say only 100 rational numbers can be inserted between 1 and 101? 4. Every Rational number is .. ...
Rectangular and triangular numbers
... Each counting number bigger than 0 is a rectangular number. The Greeks used the term rectangular number for the product of two consecutive numbers only, e.g. 42 = 6 x 7. When we draw rectangular numbers, they will look like this: ___ ...
... Each counting number bigger than 0 is a rectangular number. The Greeks used the term rectangular number for the product of two consecutive numbers only, e.g. 42 = 6 x 7. When we draw rectangular numbers, they will look like this: ___ ...
Natural (or Counting) Numbers
... Another famous irrational number is (pi). Even though it is more commonly known as 3.14, that is a rounded value for pi. Actually it is 3.1415927... It would keep going and going and going without any real repetition or pattern. In other words, it would be a non terminating, non repeating decimal, w ...
... Another famous irrational number is (pi). Even though it is more commonly known as 3.14, that is a rounded value for pi. Actually it is 3.1415927... It would keep going and going and going without any real repetition or pattern. In other words, it would be a non terminating, non repeating decimal, w ...
Sets of Real Numbers (0-2)
... Repeating Decimals • Any repeating decimal can be written as a fraction. • Write 0.8 as a fraction in simplest form. – Step 1: Let N represent the repeating decimal. Since only one digit repeats, multiply each side by 10 (If two digits repeat multiply by 100, for three multiply by 1000, etc.). Simp ...
... Repeating Decimals • Any repeating decimal can be written as a fraction. • Write 0.8 as a fraction in simplest form. – Step 1: Let N represent the repeating decimal. Since only one digit repeats, multiply each side by 10 (If two digits repeat multiply by 100, for three multiply by 1000, etc.). Simp ...
The Imaginary Numbers and the Complex
... according to the definition of imaginary numbers, we obtain -3 + 7i - 2(-1) = 3 + 7i + 2 = -1+7i. Division there is no need to talk about here (one first prolongs with the conjugate quantity of the denominator). Now I hope that the term ”complex numbers” not sounds so mystical anymore. The important ...
... according to the definition of imaginary numbers, we obtain -3 + 7i - 2(-1) = 3 + 7i + 2 = -1+7i. Division there is no need to talk about here (one first prolongs with the conjugate quantity of the denominator). Now I hope that the term ”complex numbers” not sounds so mystical anymore. The important ...
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.