Proofs - CSS342: Proofs Professor: Munehiro Fukuda CSS342:...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
CSS342: Proofs 1 CSS342: Proofs Professor: Munehiro Fukuda
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CSS342: Proofs 2 Terminologies Axioms: are assumed true. Ex: Given two distinct points, there is exactly one line that contains them. Undefined terms: implicitly defined (and used) by the axioms. Ex: Points, lines Definitions: used to create new concepts. Ex: Two lines are parallel if they never cross each other. Theorem: a proposition that has been proved to be true. If two sides of a triangle are equal, the angles opposite them are equal. Corollary: a theorem that follows quickly from another theorem. Ex: If a triangle is equilateral, then it is equiangular. Lemma: a theorem not interesting but useful in proving another theorem. Ex: A positive integer – 1 ≥ 0
Background image of page 2
CSS342: Proofs 3 Axioms, Definitions, and Undefined Terms Examples Euclidean geometry: Axiom 1: Given two distinct points, there is exactly one line that contains them. Axiom 2: If three points are not collinear, then there is exactly one plane that contains them. Definition 1: Two angles are supplementary if the sum of their measures is 180. Definition 2: Two lines are parallel if they never cross each other. Undefined terms: points, lines, planes, and angles Real numbers: Axiom 1: The commutative law stands up right for +-*/ operations. Axiom 2: If x and y are in a subset P, -x and –y are not in P, and x+y and xy are in P. Definition 1: P is called positive real numbers. Definition 2: Given a nonnegative real number, x and a positive integer, n, x 1/n is y satisfying y n = x Undefined terms: numbers and 0
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CSS342: Proofs 4 Theorem and Corollary Examples Theorem: If two sides of a triangle are equal, then the angles opposite
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 18

Proofs - CSS342: Proofs Professor: Munehiro Fukuda CSS342:...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online