Show me how this equation is valid

  • Thread starter oahz
  • Start date
In summary, a valid equation is one that follows the rules of mathematical operations and represents a true relationship between quantities. To check if an equation is valid, you can substitute values for the variables or use algebraic techniques to simplify and compare both sides. An equation is considered invalid if it does not follow these rules or accurately represent a relationship between quantities. An equation's validity can vary depending on the context in which it is used. To demonstrate the validity of an equation, one can provide a logical explanation, proof, or examples of its accuracy.
  • #1
oahz
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Please, hurry. It's driving me nuts
 

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  • #2
I suppose ##f \geq 0##? If so, ##y\geq x \implies yf(y) \geq xf(y)##.
 
  • #3
Seconded. Note that y takes on every value >= x, so you have basically replaced the constant x with the increasing function y in the integral.
 

What is the definition of a valid equation?

A valid equation is one that is logically sound and follows the rules of mathematical operations. It represents a true relationship between two or more quantities.

How can I check if an equation is valid?

To check if an equation is valid, you can substitute values for the variables and see if the equation holds true. You can also use algebraic techniques such as simplifying both sides of the equation and seeing if they are equal.

What does it mean for an equation to be invalid?

An invalid equation is one that does not follow the rules of mathematical operations or does not represent a true relationship between quantities. This could be due to incorrect use of operators, missing or incorrect terms, or other errors.

Can an equation be valid in one context but invalid in another?

Yes, an equation's validity can depend on the context in which it is used. For example, an equation may be valid for whole numbers but invalid for fractions. It is important to consider the context and limitations of an equation when determining its validity.

What steps can I take to show the validity of an equation?

To show the validity of an equation, you can provide a logical explanation or proof of how the equation was derived. You can also demonstrate its validity through examples or by showing that it follows the rules of mathematical operations.

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