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Anuj Dhawan

Senior Member

Joined: 22 Apr 2006
Posts: 6258
Location: Mumbai, India

Posted: Tue Aug 21, 2012 8:13 pm    Post subject: Two Equals One?

 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]  2a-2x = a+x-2x       [subtract 2x from both sides] 2(a-x) = a+x-2x       [2a-2x = 2(a-x)] 2(a-x) = a-x          [x-2x = -x]      2 = 1            [divide both sides by a-x]

dick scherrer

Site Director

Joined: 23 Nov 2006
Posts: 19270
Location: Inside the Matrix

 Posted: Tue Aug 21, 2012 8:34 pm    Post subject: Reply to: Two Equals One? Two does not = one - even for very large values of one . . .
Phrzby Phil

Active Member

Joined: 31 Oct 2006
Posts: 980
Location: Richmond, Virginia

 Posted: Tue Aug 21, 2012 8:35 pm    Post subject: And you complained last year when I owed you \$2 but gave you only \$1.
Robert Sample

Global Moderator

Joined: 06 Jun 2008
Posts: 8437
Location: Dubuque, Iowa, USA

 Posted: Tue Aug 21, 2012 8:36 pm    Post subject: Now, Dick, if you divide by zero as Anuj did, anything can equal anything!
dick scherrer

Site Director

Joined: 23 Nov 2006
Posts: 19270
Location: Inside the Matrix

 Posted: Tue Aug 21, 2012 8:38 pm    Post subject: Reply to: Two Equals One? Is this Fuzzy Math . . . Maybe this explains the 2 commas in my last check . . .
Robert Sample

Global Moderator

Joined: 06 Jun 2008
Posts: 8437
Location: Dubuque, Iowa, USA

 Posted: Tue Aug 21, 2012 8:41 pm    Post subject: No fuzzy math is involved. The first line sets a equal to x. The last line divides by a-x; since a=x a-x is zero, hence the results provided.
dick scherrer

Site Director

Joined: 23 Nov 2006
Posts: 19270
Location: Inside the Matrix

Posted: Tue Aug 21, 2012 8:50 pm    Post subject: Reply to: Two Equals One?

 Quote: No fuzzy math is involved.
Nope - just makin' a funny.

The first time i saw that "equation" i believe was 8th grade . . .
GuyC

Senior Member

Joined: 11 Aug 2009
Posts: 1281
Location: Belgium

Posted: Tue Aug 21, 2012 9:02 pm    Post subject:

 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.
Robert Sample

Global Moderator

Joined: 06 Jun 2008
Posts: 8437
Location: Dubuque, Iowa, USA

 Posted: Tue Aug 21, 2012 9:08 pm    Post subject: And since 1931 Godel's incompleteness theorems show that for certain statements, we cannot know whether what we are saying is true.
Akatsukami

Global Moderator

Joined: 03 Oct 2009
Posts: 1790
Location: Bloomington, IL

Posted: Tue Aug 21, 2012 9:13 pm    Post subject:

 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...
Bill Woodger

DFSORT Moderator

Joined: 09 Mar 2011
Posts: 7314

Posted: Tue Aug 21, 2012 9:14 pm    Post subject:

 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 little-enough encouragement...
Robert Sample

Global Moderator

Joined: 06 Jun 2008
Posts: 8437
Location: Dubuque, Iowa, USA

 Posted: Tue Aug 21, 2012 9:20 pm    Post subject: Akatsukami, Bill: maybe it was NOT 1931, just a very large value of 1?
Phrzby Phil

Active Member

Joined: 31 Oct 2006
Posts: 980
Location: Richmond, Virginia

 Posted: Tue Aug 21, 2012 9:25 pm    Post subject: 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 non-Euclidean models where the parallel axiom is false in various ways.
Bill Woodger

DFSORT Moderator

Joined: 09 Mar 2011
Posts: 7314

 Posted: Tue Aug 21, 2012 9:37 pm    Post subject: Reply to: Two Equals One? 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 :-)
vasanthz

Global Moderator

Joined: 28 Aug 2007
Posts: 1624
Location: Oregon

Posted: Tue Aug 21, 2012 10:55 pm    Post subject:

 Quote: if you divide by zero

-.-
Pandora-Box

Moderator

Joined: 07 Sep 2006
Posts: 1567
Location: Andromeda Galaxy

 Posted: Tue Aug 21, 2012 10:56 pm    Post subject: Lol If a=x a-x=0 so theorem fails :-D
Anuj Dhawan

Senior Member

Joined: 22 Apr 2006
Posts: 6258
Location: Mumbai, India

Posted: Wed Aug 22, 2012 9:37 am    Post subject:

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

Senior Member

Joined: 22 Apr 2006
Posts: 6258
Location: Mumbai, India

 Posted: Wed Aug 22, 2012 11:14 am    Post subject: 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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