PDF-Countable and Uncountable Sets A set is said to be nite if is empty or there is and there

n Otherwise the set is called in64257nite Two sets and are called equinumerous written if there is a bijection A set is called countably in64257nite if We say that is countable if or is 64257nite Example 31 The sets 0 and are equinumerous In. J Hildebrand Cardinality Countable and Uncountable Sets Tool Bijections Bijection from of a set Let and be sets A bijection from to is a function that is both injective and surjective Some properties of bijections Inverse functions The inverse func 1 Basic De64257nitions A map between sets and is called a bijection if is onetoone and onto In other words If then This holds for all a b For each there is some in such that We write if there is a bijection We say that and are equivalent or and. UNCOUNTABLE NOUNS. and. SOME /ANY / NO / A LOT OF. REVISION ON. REMEMBER. . Countable. . nouns. . are. . nouns. . which. can be . counted. . . and. can be in . the. . singular. . or. Sequences and Summations - vocab. An . arithmetic progression . is a sequence of the form . a, . a+d. , a+2d, … , . a+nd. , …. with fixed a, d in . R . and varying n in . Z. >=0 . A . geometric progression . A . set. is an unordered collection of objects, called . elements. of the set. A set is said to . contain. its elements. If S and T are sets, and (x S) ->(x T) then we say that S is a . subset. Lecture 16: Nov 9. A. B. …. …. f. This Lecture. We will study how to define mappings to count.. There will be many examples shown.. Bijection rule. Division rule. More mapping. Counting Rule: Bijection. Cardinality. of Infinite Sets. There be monsters here!. At least serious weirdness!. Cardinality. Recall that the cardinality of a set is merely the number of members in a set. This makes perfect sense for finite sets, but what about infinite sets?. Discrete Math for Computer Science. February 7, . 2012. Prof. Rodger. Slides modified from Rosen. Chap 2.5-2.6. Cardinality. Definition. : The . cardinality. of a set . A. is equal to the cardinality of a set . Lecture 16: Nov 9. A. B. …. …. f. This Lecture. We will study how to define mappings to count.. There will be many examples shown.. Bijection rule. Division rule. More mapping. Counting Rule: Bijection. Definition. : The . cardinality. of a set . A. is equal to the cardinality of a set . B. , denoted . . |A| = |. B. |,. if and only if there is a one-to-one correspondence (. https://www.youtube.com/watch?v=vXM6eUSUMK4. . Countable nouns. t. hings, . objects. ,. . people. , places, etc. . ca. n . be. . counted. c. an be:. . SINGULAR:. PLURAL:. . a. . + . noun. Section. . 2.4. Cardinality. How can we compare the sizes of two sets?. If . S. = {. x.  . .   .  . : . x. 2. = 9}, then . S.  = {–3,.  . 3} and we say that . S. has two elements.. NOUNS. How to prepare a sandwich….. First…... t. omatoe. cheese. bread. m. ayonaisse. mustard. l. ettuce. ham. What do you need?. Quantity. …. How . MANY. slices of bread?. How . MUCH. cheese?. A. B. …. …. f. This Lecture. We will study how to define mappings to count.. There will be many examples shown.. Bijection rule. Division rule. More mapping. Counting Rule: Bijection. If . f. is a .