Theorem
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
Such a statement is called a theorem.true
Every statement apart from the axioms or postulates.
theorem
True
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.
True. Euclid showed that more complex geometry could be described and proven deductively from a few simple principles.
A statement which appears to be true but has not been proven to be so, is a postulate.
true
Theorem: A Proven Statement. Postulate: An Accepted Statement without Proof. They mean similar things. A postulate is an unproven statement that is considered to be true; however a theorem is simply a statement that may be true or false, but only considered to be true if it has been proven.
theorem
A deductively valid argument is if the premises are true then the conclusion is certainly true, not possibly true. The definition does not say that the conclusion is true.
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 good postulate is a statement which appears to be true, and perhaps can be shown to be true in simple cases, but which has not yet been proven.
A claim is a statement that asserts something to be true, but may not necessarily be proven. A fact, on the other hand, is a statement that is proven to be true through evidence or data.