Upcoming SlideShare
×

# Math Project

4,963 views
4,762 views

Published on

Published in: Education, Technology
1 Like
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
4,963
On SlideShare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
81
0
Likes
1
Embeds 0
No embeds

No notes for slide
• ### Math Project

1. 1. Real Numbers
2. 2. Real Numbers By Kristle Wilson
3. 3. By Kristle Wilson
4. 4. What are Natural Numbers
5. 5. What are Natural Numbers In math, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional deﬁnition or the set of non-negative integers {0, 1, 2, ...} according to a deﬁnition ﬁrst appearing in the nineteenth century.
6. 6. What are Natural Numbers In math, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional deﬁnition or the set of non-negative integers {0, 1, 2, ...} according to a deﬁnition ﬁrst appearing in the nineteenth century. Natural numbers have two main purposes: counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of
7. 7. What are Natural Numbers Natural numbers have two main purposes: counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of
8. 8. What are Natural Numbers
9. 9. What Is a Whole Number
10. 10. The term whole number does not have a Real definition. Various authors use it in one of the following senses:
11. 11. The term whole number does not have a Real definition. Various authors use it in one of the following senses: ■ the nonnegative integers (0, 1, 2, 3, ...)
12. 12. The term whole number does not have a Real definition. Various authors use it in one of the following senses: ■ the nonnegative integers (0, 1, 2, 3, ...) ■ the positive integers (1, 2, 3, ...)
13. 13. The term whole number does not have a Real definition. Various authors use it in one of the following senses: ■ the nonnegative integers (0, 1, 2, 3, ...) ■ the positive integers (1, 2, 3, ...) ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
14. 14. ■ the nonnegative integers (0, 1, 2, 3, ...) ■ the positive integers (1, 2, 3, ...) ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
15. 15. ■ the positive integers (1, 2, 3, ...) ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
16. 16. ■ all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).
17. 17. What Are Integers
18. 18. S: (n) integer, whole number (any of the natural numbers (positive or negative) or zero) "an integer is a number that is not a fraction"
19. 19. What is A real Number
20. 20. In Math the real numbers may be described informally in several different ways. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an inﬁnite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real numbers may be thought of as points on an inﬁnitely long number line.
21. 21. Rational Numbers
22. 22. In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient).
23. 23. In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient). Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0.
24. 24. In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient). Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0. The decimal expansion of a rational number always either terminates after ﬁnitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base.
25. 25. In Math, a rational number is any number that can be expressed as the quotient a/b of t wo integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer corresponds to a rational number. The set of all rational numbers is usually denoted (for quotient). Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0. The decimal expansion of a rational number always either terminates after ﬁnitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
26. 26. Formally each rational number corresponds to an equivalence class. The space , where × denotes the Product, consists of all ordered pairs (m,n) where m and n are integers with n ≠ 0. The rational numbers are given by the quotient space where the equivalence relation is given by (m1,n1) ~ (m2,n2) if, and only if, m1n2 - m2n1 = 0. The decimal expansion of a rational number always either terminates after ﬁnitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
27. 27. The decimal expansion of a rational number always either terminates after ﬁnitely many digits or begins to repeat the same sequence of digits over and over. However, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
28. 28. A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost every real number is irrational.
29. 29. What Is A Irrational
30. 30. A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational.
31. 31. A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational. In abstract algebra, the rational numbers form a ﬁeld. This is the archetypical ﬁeld of characteristic zero, and is the ﬁeld of fractions for the ring of integers. Finite extensions of are called algebraic number ﬁelds, and the algebraic closure of is the ﬁeld of algebraic numbers.
32. 32. A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational. In abstract algebra, the rational numbers form a ﬁeld. This is the archetypical ﬁeld of characteristic zero, and is the ﬁeld of fractions for the ring of integers. Finite extensions of are called algebraic number ﬁelds, and the algebraic closure of is the ﬁeld of algebraic numbers.
33. 33. A real number !at " not rational " called irrational. Irrational numbers include √2, π, and e. &e decimal expansion of an irrational number continues forever wi!(t repeating. Since ) set of rational numbers " c(ntable, and ) set of real numbers " unc(ntable, almo* every real number " irrational. In abstract algebra, the rational numbers form a ﬁeld. This is the archetypical ﬁeld of characteristic zero, and is the ﬁeld of fractions for the ring of integers. Finite extensions of are called algebraic number ﬁelds, and the algebraic closure of is the ﬁeld of algebraic numbers.
34. 34. In abstract algebra, the rational numbers form a ﬁeld. This is the archetypical ﬁeld of characteristic zero, and is the ﬁeld of fractions for the ring of integers. Finite extensions of are called algebraic number ﬁelds, and the algebraic closure of is the ﬁeld of algebraic numbers.
35. 35. Chart Irrational Rational Integers Whole Natural
36. 36. Bibliography
37. 37. Bibliography
38. 38. Bibliography http://en.wikipedia.org/wiki/Natural_number
39. 39. Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number
40. 40. Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer
41. 41. Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number
42. 42. Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
43. 43. Bibliography http://en.wikipedia.org/wiki/Natural_number http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
44. 44. Bibliography http://en.wikipedia.org/wiki/Whole_number http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
45. 45. Bibliography http://wordnetweb.princeton.edu/perl/webwn?s=integer http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
46. 46. Bibliography http://en.wikipedia.org/wiki/Real_number http://en.wikipedia.org/wiki/Rational_numbers
47. 47. Bibliography http://en.wikipedia.org/wiki/Rational_numbers
48. 48. Bibliography
49. 49. Bibliography