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What statement applies to theorems?
Must Be Proved Before They Can Be Accepted As True
Can a counterexample prove that the angles of a triangle need not add up to 180 degrees?
Yes - if such a counterexample can be found. However, using only the Euclidean axioms and logical arguments, it can be proven that the angles of a triangle in a Euclidean plane must add to 180 degrees. Consequently, a counterexample within this geometry cannot exist.
What must data have to have a meaning?
a meaning
What is Godel's incompleteness theory?
Gödel's incompleteness theorem was a theorem that Kurt Gödel proved about Principia Mathematica, a system for expressing and proving statements of number theory with formal logic. Gödel proved that Principia Mathematica, and any other possible system of that kind, must be either incomplete or inconsistent: that is, either there exist true statements of number theory that cannot be proved using the system, or it is possible to prove contradictory statements in the system.
Does a postulate need to be proved?
yes no. ( a second opinion) A postulate is assumed without proof. Postulate is a word used mostly in geometry. At one time, I think people believed that postulates were self-evident . In other systems, statements that are assumed without proof are called axioms. Although postulates are assumed when you make mathematical proofs, if you doing applied math. That is, you are trying to prove theorems about real-world systems, then you have to have strong evidence that your postulates are true in the system to which you plan to apply your theorems. You could then say that your postulates must be "proved" but this is a different sense of the word than is used in mathematical proving.
