Actuarial Outpost A real proof: Two negatives equal a positive
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#1
06-15-2009, 07:33 PM
 Noumenon84 Philosopher King Join Date: Jan 2009 Studying for FAP.... eventually Posts: 954
A real proof: Two negatives equal a positive

let x = a*b + -a*b + -a*-b

x = b( a + -a) + -a*-b
x = b(0) + -a*-b
x = -a*-b

x = a*b + -a(b + -b)
x = a*b + -a(0)
x = a*b

-a*-b = a*b

I figured for every paradoxical "proof", the world needs to be balanced out by an actual proof.
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#2
06-15-2009, 07:36 PM
 The Drunken Actuary Member Join Date: Nov 2001 Favorite beer: Early and Often Posts: 66,489

Thanks!
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#3
06-15-2009, 11:16 PM
 Bamafan Member SOA AAA Join Date: Oct 2005 Location: Sabanation Studying for Life after exams Posts: 2,526

how do you know that a*b is positive?
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#4
06-15-2009, 11:40 PM
 Noumenon84 Philosopher King Join Date: Jan 2009 Studying for FAP.... eventually Posts: 954

To prove anything in life, nay to have any system of logic you must start with axioms that need no proof. However, this one can be empirically demonstrated from the definition of multiplication. Therefore it needs no thorough logical argument.
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Sum ergo Cogito

P FM MLC MFE C
#5
06-16-2009, 12:30 AM
 The Drunken Actuary Member Join Date: Nov 2001 Favorite beer: Early and Often Posts: 66,489

Quote:
 Originally Posted by Noumenon84 To prove anything in life, nay to have any system of logic you must start with axioms that need no proof. However, this one can be empirically demonstrated from the definition of multiplication. Therefore it needs no thorough logical argument.
What does it mean to multiply a negative number by a negative number? I mean, you know, by the definition of multiplication.
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I think the dollar will crash irreparably by 2012.... bottom drops out of the dollar. ....Dollars are worthless, 401ks are bust, the markets are valueless...government assumes control over all industry and everything is nationalized by the end of 2012. - gomer_tree
#6
06-16-2009, 12:33 AM
 Luda Guest Posts: n/a

Quote:
 Originally Posted by Noumenon84 To prove anything in life, nay to have any system of logic you must start with axioms that need no proof. However, this one can be empirically demonstrated from the definition of multiplication. Therefore it needs no thorough logical argument.
Are you just stringing together words because you like the way they sound? Because otherwise what you said makes no sense at all, and just makes you sound like an ignorant ass trying to trick people into thinking that you know what you're talking about. Seriously, who do you fool with this kind of crap?
#7
06-16-2009, 12:34 AM
 Vorian Atreides Wiki/Note Contributor CAS Join Date: Apr 2005 Location: Garroting Deep Studying for CAS Exam 7 College: Hard Knocks Favorite beer: Sam Adams Cherry Wheat Posts: 27,765

So what is the definition of multiplication in the case of -a*-b? For simplicity, assume that both a and b are positive.
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#8
06-16-2009, 12:36 AM
 Vorian Atreides Wiki/Note Contributor CAS Join Date: Apr 2005 Location: Garroting Deep Studying for CAS Exam 7 College: Hard Knocks Favorite beer: Sam Adams Cherry Wheat Posts: 27,765

I would also like a proof that a value that is right multiplied can be left-factored.

And if you think that what I wrote is garbage, just consider matrix multiplication.

.
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I find your lack of faith disturbing.

Wait until you have kids.

Freedom of speech is not a license to discourtesy
#9
06-16-2009, 12:44 AM
 Vorian Atreides Wiki/Note Contributor CAS Join Date: Apr 2005 Location: Garroting Deep Studying for CAS Exam 7 College: Hard Knocks Favorite beer: Sam Adams Cherry Wheat Posts: 27,765

Quote:
 Originally Posted by Noumenon84 To prove anything in life, nay to have any system of logic you must start with axioms that need no proof. However, this one can be empirically demonstrated from the definition of multiplication. Therefore it needs no thorough logical argument.
1. It's not that the axiom needs no proof but rather they're assumed to be true (or given). If it so happens that one axiom is the logical result of the other axioms in the system, then at least one of the axioms is redundant and should be removed as unnecessary luggage.

2. So what are the axioms from which you're working?

3. And (as someone else queried), how does one demonstrate empirically the multiplication of two negative numbers?
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The Search is about to begin . . . There is still time left to join.

I find your lack of faith disturbing.

Wait until you have kids.

Freedom of speech is not a license to discourtesy
#10
06-16-2009, 12:44 AM
 Luda Guest Posts: n/a

A counterexample:

Quaternions:

i^2 = j^2 = k^2 = ijk = -1

=>

(-j)*(-i) = -k

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