well.......Its like testing a conjecture and finding a statement true or false because u have to test it!!! to see if its true or false and its different,true is like something u can prove and false is untrue and u cant prove it. :D i know i don't make sense but that's how i explained it on my homeworklol
it is called a conjecture
Counterexample
Conjecture: a statement which may or may not be true.Postulate: a statement that is believed to be true, but may not be.Theorem: a statement that has been proved to be true provided some postulates are true.Corollary: a statement whose truth follows from the truth of a theorem, but one which is not important enough to call it a theorem.
To prove a statement false, you need ONE example of when it is not true.To prove it true, you need to show it is ALWAYS true.
a conjecture
well.......Its like testing a conjecture and finding a statement true or false because u have to test it!!! to see if its true or false and its different,true is like something u can prove and false is untrue and u cant prove it. :D i know i don't make sense but that's how i explained it on my homeworklol
Prove that if it were true then there must be a contradiction.
There are only two possible outcomes in finding out whether a statement is true or false.In testing a conjecture, even one contradiction is sufficient to disprove it. However, it can never be proven. All you can do is add support to the likelihood that the conjecture is true. But there remains a possibility that some other test will prove it false.Furthermore, in view of Godel's incompleteness theorem, some conjectures cannot be proven to be true even if you can prove that their negation is false.
Find one counterexample to negate the statement
it is called a conjecture
Counterexample
A statement in maths is true only if it is proved by a series of mathematical manipulations and logic for any GENERAL number for which the statement should satisfy. Otherwise, it is only a conjecture. This is the beauty of mathematics and it is proof which differentiate mathematics from all other fields.
Theorem
Conjecture: a statement which may or may not be true.Postulate: a statement that is believed to be true, but may not be.Theorem: a statement that has been proved to be true provided some postulates are true.Corollary: a statement whose truth follows from the truth of a theorem, but one which is not important enough to call it a theorem.
To prove by contradiction, you assume that an opposite assumption is true, then disprove the opposite statement.
To prove a statement false, you need ONE example of when it is not true.To prove it true, you need to show it is ALWAYS true.