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September 5th, 2010, 10:46 PM  #1 
Newbie Joined: Sep 2010 Posts: 1 Thanks: 0  Probably the simplest question of all time.
When simplifying an equation, if all like terms cancel out, is the final answer 1 or 0?

September 6th, 2010, 11:06 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Probably the simplest question of all time.
It depends what kind of cancellation it is: x/x = 1 xx = 0 
September 7th, 2010, 10:19 AM  #3 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Probably the simplest question of all time.
aswoods is obviously right  I'll just elaborate a little. If you have something like 2x + 7 = 2x + 7, then you can "cancel" the 2x AND the 7 from both sides and be left with 0 = 0. If you subtracted 2x and 7 from both sides, you would have (2x + 7 )  (2x + 7) = 0 0 = 0. Redundant... maybe! One significant observation about this equation is that ANY NUMBER makes it a true statement. Actually, the statement is just plain true (at least in ZFC ) But if you have something like 3x + 7  3x  7 = 5, then you get 0 = 5, which is FALSE, regardless of what value for x you choose. So while all of the stuff on the left canceled, there was still something on the right. 
September 7th, 2010, 11:34 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  Re: Probably the simplest question of all time.
When solving simultaneous systems of equations, the two scenarios given by The Chaz may arise. Suppose you are given: x  2y = 3 6y  3x = 9 Solving the first equation for x gives x = 2y + 3. Substituting this into the second equation, we have 6y  3(2y + 3) = 9 6y  6y  9 = 9 0 = 0 When this occurs, it is because the second equation is derived from the first, scaled by a factor of 3, and this system is said to be dependent. The two equations describe the same relationship between x and y, possess the same graph in the xyplane, thus all real values for x and y satisfy the system. Now, consider the following system x  3y = 2 12y  4x = 9 Solving the first equation for x gives x = 3y + 2. Substituting this into the second equation, we have 12y  4(3y + 2) = 9 12y  12y  8 = 9 1 = 0 This is a false statement, so we must assume the system has no solution. If we graph these two equations, we will find that they are distinct parallel lines and will have no point of intersection, at least in Euclidean geometry. This system is said to be inconsistent. 
September 7th, 2010, 12:53 PM  #5 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Probably the simplest question of all time.
You and your fancypants parallel postulate...


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