Every statement apart from the axioms or postulates.
False. It is proven to be true IF some axioms are assumed to be true. A mathematical statement can be proven to be true only after some axioms have been assumed.
theorem
Theorem
Such a statement is called a theorem.true
The statement is false.
Theorem
A conjecture is an unproven statement or hypothesis that is proposed based on observations or patterns. When a conjecture is proven true through logical reasoning or mathematical proof, it becomes a theorem. For example, the conjecture that "the sum of the angles in a triangle is always 180 degrees" is a statement that can be proven true in Euclidean geometry.
It must be proven to be true by several different individuals not known to each other.
False. It is proven to be true IF some axioms are assumed to be true. A mathematical statement can be proven to be true only after some axioms have been assumed.
A true statement that can be proven is that the sum of the interior angles of a triangle is always 180 degrees. This can be demonstrated through various methods, such as using parallel lines and transversals or by employing geometric proofs. Regardless of the type of triangle—whether it is scalene, isosceles, or equilateral—this rule holds true universally in Euclidean geometry.
True
theorem
hypothesis
postulates
An objective statement is based on facts and can be proven true or false, while a subjective statement is based on personal opinions or feelings and cannot be proven true or false.
A statement that can be proven true or false. Not a question, not a command, and not an opinion.
A statement which appears to be true but has not been proven to be so, is a postulate.