May 17th, 2017, 12:23 AM  #1 
Senior Member Joined: Nov 2011 Posts: 109 Thanks: 1  Who is bigger?
Who is bigger > the all of the possible equations set or all the possible graphs set in cartesian XYZ graph?

May 17th, 2017, 03:59 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,820 Thanks: 750 
Define precisely what you mean by an "equation". It can be argued that if two "different" equations have exactly the same graph, then one can be reduced to the other so the are really the "same" equation. To avoid confusion, you have to say exactly what is meant by "different" and "same" equation.

May 17th, 2017, 05:26 AM  #3 
Senior Member Joined: Nov 2011 Posts: 109 Thanks: 1 
rI mean: All the equation that exist (until the maximum that possible) All the graphs you can draw and possible equation = variables with operations. I don't find a definition that precisely example of what or what not is equation? Can you define the mathematical term of equation and from this point to go further to answer my question? 
May 17th, 2017, 06:09 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,820 Thanks: 750 
My point was to get you to tell us what you mean by "equation" and what you would consider as two different equations when counting them. For example, the "equation" x +y= 3 and the "equation" 2x+ 2y= 6 have exactly the same graph, the straight line determined by (3, 0) and (0, 3). When counting equations would you consider those two different equations or just variations of the same equation? If you consider them two different equations, then there are far more "equations" than "graphs" since many different equations that give the same graph. If you consider "x+ y= 3" and "2x+ 2y= 6" the same equation because they are satisfied by the same (x, y) pairs, then their are exactly the same number of equations as graphs because a graph is, simply, a collection of (x, y) pairs.

May 17th, 2017, 06:22 AM  #5 
Senior Member Joined: Nov 2011 Posts: 109 Thanks: 1 
Nice. Thanks.


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