A statement that can be proved true is a mathematical proposition such as "The sum of two even numbers is always even." This can be demonstrated through logical reasoning or examples, as any two even integers can be represented as 2n and 2m (where n and m are integers), and their sum (2n + 2m) is 2(n + m), which is also an even number. Thus, the statement holds true under the rules of arithmetic.
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Must Be Proved Before They Can Be Accepted As True
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observation proved the theory true.
Must Be Proved Before They Can Be Accepted As True
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A statement that can be proved to be true or false is known as a proposition in logic. For example, the statement "The Earth orbits the Sun" is a proposition that can be verified as true. Conversely, the statement "All swans are white" can be proven false by the existence of black swans. These statements are distinct from opinions or questions, which cannot be categorized as true or false.
An axiom is a self-evident statement that is assumed to be true. A theorem is proved to be true.
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