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There are many kinds of statement that are not theorems: A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be. A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication. A statement can be false. A statement can be self-contradictory for example, "This statement is false".
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Something like "Write a false statement".
It is a question that is definitely true or definitely false. It can't be both.
Yes, a statement can be true or false but without knowing what the statement is no-one can possibly say whether it is true or it is false.
The below statement is false. The above statement is true. I am lying. I am lying when I say I am lying.
Statements that are self contradictory are paradoxes or oxymorons. Some are trivial some are funny. A funny one would be military intelligence or military music. A more serious one is the old one about an immovable object and an irresistible force
Statements that are self contradictory are paradoxes or oxymorons. Some are trivial some are funny. A funny one would be military intelligence or military music. A more serious one is the old one about an immovable object and an irresistible force
There are many kinds of statement that are not theorems: A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be. A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication. A statement can be false. A statement can be self-contradictory for example, "This statement is false".
One classic example of a paradox is the "liar paradox," which revolves around a statement that cannot consistently be true or false. An example would be the statement "This statement is false." If the statement is true, then it must be false, but if it is false, then it must be true, creating a paradoxical situation.
Self-contradictory statements are called paradoxes. They are seemingly true, but lead to a logical inconsistency or contradiction when examined closely. Some famous examples include "This statement is false" and "I always lie."
A contradictory proposition is a proposition that contains a contradiction and therefore is false.
One classic example of a paradox is the "liar paradox." It is a statement that asserts its own falsehood, such as "This statement is false." If the statement is true, then it must be false, but if it is false, then it must be true, leading to a contradictory situation.
The statement "less is more" is a paradox because it combines two contradictory ideas. The grandfather paradox is a hypothetical situation where someone could potentially travel back in time and prevent their own existence, creating a paradox because their existence would be both necessary and impossible at the same time. The liar paradox is a statement such as "this statement is false," which creates a contradiction when considering its truth value.
Something like "Write a false statement".
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If the statement is false, then "This statement is false", is a lie, making it "This statement is true." The statement is now true. But if the statement is true, then "This statement is false" is true, making the statement false. But if the statement is false, then "This statement is false", is a lie, making it "This statement is true." The statement is now true. But if the statement is true, then... It's one of the biggest paradoxes ever, just like saying, "I'm lying right now."