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Homework Statement
prove : 0 = -0
For a real number to equal another real number, they must have the same value. In this case, both 0 and -0 have a value of 0, so they are considered equal.
Axioms are self-evident truths that serve as the basis for a mathematical system. They are used to prove mathematical statements, such as 0 = -0, by following logical steps.
Yes, it is possible to prove 0 = -0 using axioms. One way to do so is by using the axiom of identity, which states that any number is equal to itself. Since 0 and -0 both have a value of 0, they are equal to themselves.
Proving mathematical statements, such as 0 = -0, is important because it helps to establish the validity of a mathematical system. It also allows us to better understand the properties and relationships of numbers.
Yes, there are other ways to prove 0 = -0, such as using the definition of equality, which states that two numbers are equal if they have the same value and sign. Since 0 and -0 both have a value of 0 and a sign of positive, they are considered equal by definition.