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(aka axiom) A statement whose truth is accepted without proof A statement that has been proven to be true by using deductive reasoning
An axiom is a statement that is assumed to be true without any proof, while a theory is subject to be proven before it is considered to be true or false 2 An
to be accepted without proof (and even without certainty); but an axiom is Generally speaking, a theorem is some major result that you wish to prove
Lemma: A true statement used in proving other true statements (that is, a less important theorem that is helpful in the proof of other results)
We now prove Theorems A1 2 and A1 3 without analysing them Theorem A1 2 : The product of two even natural numbers is even
may also refer to axioms, which are the starting points, “rules” accepted by everyone Mathematical proof is absolute, which means that once a theorem is
meanings of three key terms: Theorem, proof and definition Another fact that we will accept without proof (at least for now) is
Demonstrative geometry is a branch of mathematics in which theorems Assumptions: Some statements are accepted true without proofs
Topic 2 – Reasoning and Proof Law of Detachment: Converse of the Alternate Interior Angles Theorem: Spherical Geometry Triangle Angle Sum Theorem