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MACM 101 Lecture 17: Lecture 17 Part 2_ Cardinality

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browncricket987

21 Dec 2018

School

Simon Fraser University

Department

Math & Comp Sci

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Professor

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Document Summary

Sets that are not countable are called uncountable countable sets: finite sets any subset of n. In other words we can make a list of all integers. 0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, . The cardinality of the set of all natural numbers is denoted by 0. The set of positive rational numbers is countable. Every rational number can be represented as a fraction p/q. We do not insist that p and q do not have a common divisor. This gives an injection from q+ to n. the converse injection is f(x) = x + 1. If a is an infinite set, then | a | 0. Every real number can be represented as an infinite decimal fraction, like. Suppose we have constructed a list of all real numbers. Let bi = 4 if aii 4.

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Related Questions

Consider the integers with the normal operation of addition.

On which of these subsets of the integers is addition "closed" ? (select all that are correct)

a)	The natural numbers: {1, 2, 3, ... }

b)	The multiples of 3: {..., -6, -3, 0, 3, 6, ...}

c)	The odd integers: {..., -3, -1, 1, 3, 5, ...}

d)	The nonnegative integers less than 5: {0, 1, 2, 3, 4}

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