Fairy111 said:Homework Statement
For real numbers x(1), x(2), ..., x(n), prove that |x(1) + x(2) +...+x(n)| <= |x(1)|+...|(n)|
Real numbers are numbers that can be found on the number line and include positive and negative whole numbers, fractions, decimals, and irrational numbers like pi and square root of 2.
To prove a statement using real numbers, you must provide evidence or logical steps that show the statement is true for all real numbers. This can include using algebraic equations, geometric proofs, or logical reasoning.
Yes, for example, to prove that the sum of two even numbers is always an even number, we can use real numbers such as 4 and 6. The sum of 4 and 6 is 10, which is also an even number. This holds true for all even numbers, therefore the statement is proven.
Proofs with real numbers are important in mathematics and science because they provide a way to validate theories and statements. They allow us to show that a statement is true for all possible values of real numbers and can help us make predictions and solve problems.
Yes, there are limitations to proofs with real numbers. They may not apply to all situations, such as when dealing with complex or imaginary numbers. Additionally, some statements may be difficult or impossible to prove using real numbers alone and may require other mathematical concepts.