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Announcement: new book being written (by me!)


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#81 Merlin Jetton

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Posted 30 March 2013 - 01:17 PM

That is why I no longer strenuously argue the shape of the Earth with members of the Flat Earth Society.

 

Here is a summary of Hilbert's accomplishments,  that "religious nut".

 

http://en.wikipedia....i/David_Hilbert

 

I have never been a member of the Flat Earth Society.

 

Here is a summary of Henri Poincaré's accomplishments (link).

 

Still clinging to your faulty premise, eh?



#82 BaalChatzaf

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Posted 31 March 2013 - 08:49 AM

That is why I no longer strenuously argue the shape of the Earth with members of the Flat Earth Society.

 

Here is a summary of Hilbert's accomplishments,  that "religious nut".

 

http://en.wikipedia....i/David_Hilbert

 

I have never been a member of the Flat Earth Society.

 

Here is a summary of Henri Poincaré's accomplishments (link).

 

Still clinging to your faulty premise, eh?

Both Poincare and Hilbert were top mathematicians in the late 19 th and early 20 th century.

 

Ba'al Chatzaf 


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#83 BaalChatzaf

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Posted 24 August 2013 - 09:24 AM

 

wrong.  The integers can be put into 1 - 1 correspondence with the even integers.  That means the set of integers and the set of even integers have the same cardinality.   

 

Unstated false premise -- the only way to compare quantities is 1-1 correspondence.

 

Mis-speak.  -A- way of comparing quantities is a 1-1 correspondence.  

 

If you have another and it is logically consistent,  then use it.  As long as 2 + 2 = 4  it is cool.

 

Ba'al Chatzaf 


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#84 Merlin Jetton

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Posted 24 August 2013 - 10:57 AM

 

-A- way of comparing quantities is a 1-1 correspondence.  

 

If you have another and it is logically consistent,  then use it.  As long as 2 + 2 = 4  it is cool.

 

y = x if x even, x+1 if x odd. That is a 2-to-1 map/function/correspondence, which implies the set X (all integers) has twice as many numbers as the set Y (even integers).



#85 BaalChatzaf

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Posted 24 August 2013 - 12:55 PM

 

wrong.  The integers can be put into 1 - 1 correspondence with the even integers.  That means the set of integers and the set of even integers have the same cardinality.   

 

Unstated false premise -- the only way to compare quantities is 1-1 correspondence.

 

Who said it was the -only- way.  It is -a way-.  If you define equi cardinality as the existence of a 1-1 onto mapping between sets then this relation has the three properties  that any righteous equivalency has:  it is reflexive, symmetry and transitive. 

 

If you know another definition of equality between objects (please specify which objects)  then pray do let us know what you have in mind. 

 

As long as what you come up with leads to no contradictions and has the three properties of a righteous equivalence you are o.k.

 

Let us know what you had in mind.

 

By the way,  if you restrict cardinal quantities to the cardinals of finite sets (no matter how) large  you will not  get the feature that a set can be put in 1-1 correspondence with a proper subset of itself.  So if you want quantities that a proper Objectivist  would not Object to,  then restrict yourself to finite sets.

 

Ba'al Chatzaf 


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#86 BaalChatzaf

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Posted 24 August 2013 - 01:00 PM

 

 

-A- way of comparing quantities is a 1-1 correspondence.  

 

If you have another and it is logically consistent,  then use it.  As long as 2 + 2 = 4  it is cool.

 

y = x if x even, x+1 if x odd. That is a 2-to-1 map/function/correspondence, which implies the set X (all integers) has twice as many numbers as the set Y (even integers).

 

That is ill defined. What are two sets and what is the mapping.;

 

Let the two sets  be A and B,  both subsets of the integers. 

 

Now let x in A.  If x is even you say  f(x) = x

 

and if x is odd you say f(x) = x + 1.

 

if x = x'  then f(x) = f(x')   now let us check the -inverse-

 

suppose   f(x) = f(x')   does this imply x = x'.  No   

 

Example f(4)  = 4  but f(3)  = 4  so the inverse function is not well defined. 

 

So, 4 and 3 which are not equal get mapped into  the same element.  bzzzzzzzt.  Wrong.  

 

So your function as you defined it is NOT a 1-1  onto mapping.  It has an ill defined inverse.

 

Go back and try something else.

 

or take a course in algebra or set theory.

 

Do something useful.

 

Ba'al Chatzaf


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#87 Merlin Jetton

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Posted 24 August 2013 - 01:46 PM

 

That is ill defined. What are two sets and what is the mapping.;

 

Let the two sets  be A and B,  both subsets of the integers. 

 

Now let x in A.  If x is even you say  f(x) = x

 

and if x is odd you say f(x) = x + 1.

 

if x = x'  then f(x) = f(x')   now let us check the -inverse-

 

suppose   f(x) = f(x')   does this imply x = x'.  No   

 

Example f(4)  = 4  but f(3)  = 4  so the inverse function is not well defined. 

 

So, 4 and 3 which are not equal get mapped into  the same element.  bzzzzzzzt.  Wrong.  

 

So your function as you defined it is NOT a 1-1  onto mapping.  It has an ill defined inverse.

 

 

Wrong. Of course, it is not a 1-to-1 mapping. I clearly said it was a 2-to-1. What's next, f(x)=x^2 isn't well-defined because both x=2 and x=-2 map to the same element, 4?

 

Go back and try something else. Do something useful.



#88 BaalChatzaf

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Posted 24 August 2013 - 02:05 PM

 

 

That is ill defined. What are two sets and what is the mapping.;

 

Let the two sets  be A and B,  both subsets of the integers. 

 

Now let x in A.  If x is even you say  f(x) = x

 

and if x is odd you say f(x) = x + 1.

 

if x = x'  then f(x) = f(x')   now let us check the -inverse-

 

suppose   f(x) = f(x')   does this imply x = x'.  No   

 

Example f(4)  = 4  but f(3)  = 4  so the inverse function is not well defined. 

 

So, 4 and 3 which are not equal get mapped into  the same element.  bzzzzzzzt.  Wrong.  

 

So your function as you defined it is NOT a 1-1  onto mapping.  It has an ill defined inverse.

 

 

Wrong. Of course, it is not a 1-to-1 mapping. I clearly said it was a 2-to-1. What's next, f(x)=x^2 isn't well-defined because both x=2 and x=-2 map to the same element, 4?

 

Go back and try something else. Do something useful.

 

Why not a 3 to 


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