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f_x_ = the _biological_ mother of x

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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
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