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1 Example Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x Since everybody has a mother (one and only one) , f is a function. 1 Example Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x Since everybody has a mother (one and only one) , f is a function. Question • Take any person, call him or her x0. 1 Example Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x Since everybody has a mother (one and only one) , f is a function. Question • Take any person, call him or her x0. • Let x1 = f (x0), that is, x1 is the mother of x0. 1 Example Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x Since everybody has a mother (one and only one) , f is a function. Question • Take any person, call him or her x0. • Let x1 = f (x0), that is, x1 is the mother of x0. • Let x2 = f (x1), that is, x2 is the mother of x1. 1 Example Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x Since everybody has a mother (one and only one) , f is a function. Question • Take any person, call him or her x0. • Let x1 = f (x0), that is, x1 is the mother of x0. • Let x2 = f (x1), that is, x2 is the mother of x1. • Because everyone has a mother, we can repeat the above process indeﬁnitely to get a sequence (“family tree”) x0, x1, x2, x3, x4, x5, . . . 1 Example Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x Since everybody has a mother (one and only one) , f is a function. Question • Take any person, call him or her x0. • Let x1 = f (x0), that is, x1 is the mother of x0. • Let x2 = f (x1), that is, x2 is the mother of x1. • Because everyone has a mother, we can repeat the above process indeﬁnitely to get a sequence (“family tree”) x0, x1, x2, x3, x4, x5, . . . This implies that there are inﬁnitely many human beings. But , history of mankind is ﬁnite, so there are only ﬁnitely many human beings. 2 Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x What’s wrong? 2 Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x What’s wrong? • May be the statement “everybody has a mother ” is incorrect. Thus f is not a function (some inputs do not give any output ). 2 Let H be the set of all human beings, deceased or alive. Let f : H −→ H be the function given by f (x) = the (biological) mother of x What’s wrong? • May be the statement “everybody has a mother ” is incorrect. Thus f is not a function (some inputs do not give any output ). • Or H is not a set; there may be something between human and non-human.

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posted: | 5/15/2010 |

language: | English |

pages: | 9 |

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