Circular Reasoning and Impossible Equation

In summary, there is a circular dependency between x and y that makes it impossible to write a sensible equation containing both variables. However, it is still possible to write an equation, but it will not have a finite set of solutions and will instead have a large number of ordered pairs that will make it true. This can be thought of as an identity rather than an equation. Additionally, if the equations are independent, a unique solution can still be found for a specific ordered pair (x, y).
  • #1
e2m2a
354
11
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
  • #2
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!
 
  • #3
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.
 
  • #4
What if ##x = 2y## and ##y = x - 1##?
 
  • Like
Likes Mark44
  • #5
They are two independent equations and will give you the solution for a unique ordered pair (x, y).
 
  • #6
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:
 
  • #7
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.
 

1. What is circular reasoning?

Circular reasoning is a logical fallacy in which the conclusion of an argument is also used as one of the premises. This creates a circular or self-referential argument that does not provide any real evidence or support for the conclusion.

2. How can circular reasoning be identified?

Circular reasoning can be identified by looking for arguments that use the conclusion to support itself or arguments that repeat the same information in different words without providing any new evidence.

3. Can circular reasoning ever be a valid form of reasoning?

No, circular reasoning is always a logical fallacy and cannot be considered a valid form of reasoning. It does not provide any real evidence or support for the conclusion and can lead to false conclusions.

4. What is an impossible equation?

An impossible equation is a mathematical equation that has no solution or contradicts basic mathematical principles. For example, an equation that states 2 + 2 = 5 would be considered an impossible equation.

5. How can an impossible equation be identified?

An impossible equation can be identified by checking for any mathematical errors or illogical statements within the equation. It can also be identified by attempting to solve the equation and finding that it is not possible to do so.

Similar threads

B Can We Simplify the Taylor Series Expansion for e^(f(x,y))?
    • General Math
Replies
3
Views
723
I Adding 'z' to 2D graph equation
    • General Math
Replies
3
Views
1K
I Partial Differential Equation solved using Products
    • General Math
Replies
2
Views
261
I Area of a Circle: Solving the Equation
    • General Math
Replies
3
Views
804
I Plotting polar equations and scale invariance
    • General Math
Replies
7
Views
1K
MHB How to solve following optimization problem?
    • General Math
Replies
2
Views
947
I Best way to fit three functions
    • General Math
Replies
2
Views
728
I Creating a function with specific shape, intercepts, integral....
    • General Math
Replies
1
Views
801
I Quadratic, cubic, quartic, quintic equations
    • General Math
Replies
16
Views
3K
I Statistical modeling and relationship between random variables
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
459

Hot Threads

Recent Insights

Back
Top