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A theorem is a proven statement. Both lemma and corollary are (special kinds of) theorems. The "usual" difference is that a lemma is a minor theorem usually towards proving a more significant theorem. Whereas a corollary is an "easy" or "evident" consequence of another theorem (or lemma).
A Theorem is a major result. A Corollary is a theorem that follows on from another theorem. A Lemma is a small result (less important than a theorem) Examples. Here is an example from Geometry: Example: A Theorem and a Corollary. Theorem: Angles on one side of a straight line always add to 180°. Corollary:
Oct 25, 2010 · A theorem is a logical consequence of the axioms. In Geometry, the "propositions" are all theorems: they are derived using the axioms and the valid rules. A "Corollary" is a theorem that is usually considered an "easy consequence" of another theorem. What is or is not a corollary is entirely subjective.
A corollary is a theorem that “easily” follows from the preceding theorem. For example, after proving the theorem that the sum of the angles in a triangle is 180°, an easy theorem to prove is that the sum of the angles in a quadrilateral is 360°.
Jan 12, 2013 · The four labels given by mathematicians to statements that can be shown to be true are Lemma, Theorem, Proposition and Corollary. They all basically mean the same thing: some mathematical statement that is true, given some starting axioms or previous true statements.
Corollary: a true statement that is a simple deduction from a theorem or proposition. Proof: the explanation of why a statement is true. Conjecture: a statement believed to be true, but for which we have no proof. Axiom: a basic assumption about a mathematical situation (model) which requires no proof.
Example: there is a Theorem that says: two angles that together form a straight line are "supplementary" (they add to 180°). A Corollary to this is the "Vertical Angle Theorem" that says: where two lines intersect, the angles opposite each other are equal (a=c and b=d in the diagram).
In mathematics, a corollary is a theorem connected by a short proof to an existing theorem. The use of the term corollary, rather than proposition or theorem, is intrinsically subjective. More formally, proposition B is a corollary of proposition A, if B can be readily deduced from A or is self-evident from its proof.
Lemma. A lemma is a theorem that is largely proven as a prelude to the proof of another theorem. Corollary. A corollary is a theorem that naturally results from another theorem. When they are first introduced, theorems are frequently referred to as propositions. Proposition.
Corollary is a theorem which follows its statement from the other theorem. Mathematically, corollary of theorems are used as the secondary proof for a complicated theorem. It helps to apprehend the initial theorem more preciously.
