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Anuj Dhawan
Senior Member
Joined: 22 Apr 2006 Posts: 6258 Location: Mumbai, India




Code: 
a = x [true for some a's and x's]
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a2x = a+x2x [subtract 2x from both sides]
2(ax) = a+x2x [2a2x = 2(ax)]
2(ax) = ax [x2x = x]
2 = 1 [divide both sides by ax] 


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dick scherrer
Site Director
Joined: 23 Nov 2006 Posts: 19270 Location: Inside the Matrix




Two does not = one  even for very large values of one . . . 

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Phrzby Phil
Active Member
Joined: 31 Oct 2006 Posts: 962 Location: Richmond, Virginia




And you complained last year when I owed you $2 but gave you only $1. 

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Robert Sample
Global Moderator
Joined: 06 Jun 2008 Posts: 7990 Location: Bellevue, IA




Now, Dick, if you divide by zero as Anuj did, anything can equal anything! 

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dick scherrer
Site Director
Joined: 23 Nov 2006 Posts: 19270 Location: Inside the Matrix




Is this Fuzzy Math . . .
Maybe this explains the 2 commas in my last check . . . 

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Robert Sample
Global Moderator
Joined: 06 Jun 2008 Posts: 7990 Location: Bellevue, IA




No fuzzy math is involved. The first line sets a equal to x. The last line divides by ax; since a=x ax is zero, hence the results provided. 

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dick scherrer
Site Director
Joined: 23 Nov 2006 Posts: 19270 Location: Inside the Matrix




Quote: 
No fuzzy math is involved. 
Nope  just makin' a funny.
The first time i saw that "equation" i believe was 8th grade . . . 

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GuyC
Senior Member
Joined: 11 Aug 2009 Posts: 1280 Location: Belgium




Quote: 
Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing... It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true... If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. 


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Robert Sample
Global Moderator
Joined: 06 Jun 2008 Posts: 7990 Location: Bellevue, IA




And since 1931 Godel's incompleteness theorems show that for certain statements, we cannot know whether what we are saying is true. 

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Akatsukami
Global Moderator
Joined: 03 Oct 2009 Posts: 1753 Location: Bloomington, IL




Robert Sample wrote: 
And since 1931 Godel's incompleteness theorems show that for certain statements, we cannot know whether what we are saying is true. 
Suddenly all the questions asked on this forum make sense... 

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Bill Woodger
DFSORT Moderator
Joined: 09 Mar 2011 Posts: 7306




Robert Sample wrote: 
And since 1931 Godel's incompleteness theorems show that for certain statements, we cannot know whether what we are saying is true. 
Can we even be sure it was 1931? Or that we won't get that same slew of old jokes...
I need littleenough encouragement... 

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Robert Sample
Global Moderator
Joined: 06 Jun 2008 Posts: 7990 Location: Bellevue, IA




Akatsukami,
Bill: maybe it was NOT 1931, just a very large value of 1? 

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Phrzby Phil
Active Member
Joined: 31 Oct 2006 Posts: 962 Location: Richmond, Virginia




What Godel proved was that in axiom systems capable of doing at least simple arithmetic, there are statements that can neither be proven nor disproven.
"True" is not a word used in this instance.
Where "true" comes into play is when the elements the axioms define are assigned values in a model.
So the parallel axiom in geometry is independent of the "simpler" axioms  it cannot be proven from them.
In the flat Euclidean model, it is true. If one assigns other meanings to "point" and "line", then one can define nonEuclidean models where the parallel axiom is false in various ways. 

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Bill Woodger
DFSORT Moderator
Joined: 09 Mar 2011 Posts: 7306




Phr.. er, Phil, I was serious about not bringing up those old jokes.
Akatsukami, first class.
Now, with what theory do we explain the "post once then disappear"? If I can understand that one as well, I'll be happy :) 

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vasanthz
Global Moderator
Joined: 28 Aug 2007 Posts: 1474 Location: Chennai




Quote: 
if you divide by zero 
. 

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PandoraBox
Moderator
Joined: 07 Sep 2006 Posts: 1534 Location: Andromeda Galaxy




Lol
If a=x
ax=0
so theorem fails :D 

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Anuj Dhawan
Senior Member
Joined: 22 Apr 2006 Posts: 6258 Location: Mumbai, India




Akatsukami wrote: 
Suddenly all the questions asked on this forum make sense... 
ROFL, Good one! 

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Anuj Dhawan
Senior Member
Joined: 22 Apr 2006 Posts: 6258 Location: Mumbai, India




10/10 Robert  now I understand why one should NOT mess with a mathematic'student!
As GuyC quoted: "if such and such a proposition is true of anything, then such and such another proposition is true of that thing"
It's similar to an invalid proof: 2 × 0 = 1 × 0 (which is true), one can divide by zero to obtain 2 = 1. Divide by zero is not defined in math (infinity, a concept. Perhaps pretty similar to NULL, the way we discuss that here). 

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