chehada assaf
a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific theory.
postulate: A postulate is a statement that is accepted without proof.Axiom is another name for postulate. For example, if you know that Pam is 5-feet tall and all her siblings are taller than her, you would believe her if she said that all of her siblings is at least 5.1'. Pam just stated a postulate, and you just accepted it without grabbing a tape measure to verify the height of her siblings.
corollary: A special case of a more general theorem which is worth noting separately. For example, the Pythagorean theorem is a corollary of the law of cosines.
proposition: A proposition is a declaration that can be either true or false, but not both. For example, “Today is Friday” is a proposition. This statement can be true or false, but not both.
a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific theory.
postulate: A postulate is a statement that is accepted without proof.Axiom is another name for postulate. For example, if you know that Pam is 5-feet tall and all her siblings are taller than her, you would believe her if she said that all of her siblings is at least 5.1'. Pam just stated a postulate, and you just accepted it without grabbing a tape measure to verify the height of her siblings.
corollary: A special case of a more general theorem which is worth noting separately. For example, the Pythagorean theorem is a corollary of the law of cosines.
proposition: A proposition is a declaration that can be either true or false, but not both. For example, “Today is Friday” is a proposition. This statement can be true or false, but not both.
No comments:
Post a Comment