Circular Reasoning and Impossible Equation

  • Context: Undergrad 
  • Thread starter Thread starter e2m2a
  • Start date Start date
  • Tags Tags
    Circular Impossible
Click For Summary
SUMMARY

The discussion centers on the concept of circular reasoning in equations involving variables x and y, where each variable depends on the other. It concludes that while one can formulate equations like x = y, such equations do not yield unique solutions but rather represent identities with infinite solutions. The example of x = 2y and y = x - 1 illustrates how independent equations can provide a unique solution for the ordered pair (x, y), contrasting with the circular dependency scenario.

PREREQUISITES
  • Understanding of basic algebraic equations
  • Knowledge of variable dependency in mathematical contexts
  • Familiarity with concepts of identities versus equations
  • Ability to analyze systems of equations
NEXT STEPS
  • Explore the concept of variable dependency in mathematical modeling
  • Study systems of linear equations and their solutions
  • Learn about identities in algebra and their implications
  • Investigate the implications of circular reasoning in logic and mathematics
USEFUL FOR

Mathematicians, educators, students studying algebra, and anyone interested in the logical foundations of equations and variable relationships.

e2m2a
Messages
354
Reaction score
13
Suppose there is a problem such that in order to know a variable x, you have to know a variable y. But in order to know variable y, you have to know the variable x. Because of this circular dependency, wouldn't it be impossible to write any sensible equation containing x and y?
 
Mathematics news on Phys.org
You can definitely write an equation but you cannot get some finite set of values for x and y only for which that equation will be true it will be true for a large number of ordered pair (x,y). It will be some thing like identity and not an equation!
 
Let'sthink said:
You can definitely write an equation but you cannot get some finite set of values for x and y only for which that equation will be true it will be true for a large number of ordered pair (x,y). It will be some thing like identity and not an equation!
That makes sense. Thanks.
 
What if ##x = 2y## and ##y = x - 1##?
 
  • Like
Likes   Reactions: Mark44
They are two independent equations and will give you the solution for a unique ordered pair (x, y).
 
e2m2a said:
Suppose there is a problem such that in order to know a variable x, you have to know a variable y. But in order to know variable y, you have to know the variable x. Because of this circular dependency, wouldn't it be impossible to write any sensible equation containing x and y?
Take, for example, x=y. From this you can determine neither x nor y. Nevertheless, the equation is very sensible, i.e. contains a lot of useful information. For instance, if x is your position and y is the position of your wallet, and you are a tourist lost in Rio De Janeiro, you will be very happy to know that x=y. :smile:
 
Let'sthink said:
You can definitely write an equation but you cannot get some finite set of values for x and y only for which that equation will be true it will be true for a large number of ordered pair (x,y). It will be some thing like identity and not an equation!
fresh_42 said:
What if ##x = 2y## and ##y = x - 1##?
Let'sthink said:
They are two independent equations and will give you the solution for a unique ordered pair (x, y).
A unique solution is quite different from a solution set that is infinitely large.
 

Similar threads

Undergrad Adding 'z' to 2D graph equation
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Partial Differential Equation solved using Products
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Plotting polar equations and scale invariance
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Area of a Circle: Solving the Equation
  • · Replies 3 ·
Replies
3
Views
2K
High School A symmetric problem has an asymmetric solution - why?
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad Best way to fit three functions
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Quadratic, cubic, quartic, quintic equations
  • · Replies 16 ·
Replies
16
Views
5K
Model a ball in a moving circular bowl using Cartesian coordinates
  • · Replies 24 ·
Replies
24
Views
3K
Undergrad Creating a function with specific shape, intercepts, integral....
  • · Replies 1 ·
Replies
1
Views
1K
High School Can you perform algebra on derivatives?
  • · Replies 5 ·
Replies
5
Views
1K