Understanding the Concept of "is equal to over the set of all rational numbers"
Definition of "is equal to over the set of all rational numbers"
"Is equal to over the set of all rational numbers" means that a certain mathematical expression or equation holds true for all rational numbers.
Explanation of Rational Numbers
Rational numbers are numbers that can be expressed as a fraction of two integers. Rational numbers can be positive, negative or zero, and they can be expressed as terminating or repeating decimals. Examples of rational numbers include 3/4, -2/3, and 0.5.
Examples of "is equal to over the set of all rational numbers"
Here are some examples of mathematical expressions that are equal to over the set of all rational numbers:
1. x + 3 = 3x - 5
2. 2x + 5y = 10
3. x^2 + 4x + 4 = 0
In each of these examples, the equation is true for any rational number that is substituted for x and y. For example, in the first equation, if x is 1/2, then 1/2 + 3 = 3(1/2) - 5, which is true.
Conclusion
In conclusion, "is equal to over the set of all rational numbers" means that a certain mathematical expression or equation holds true for all rational numbers. This concept is important in many areas of mathematics, including algebra and calculus.