MATA31H3 Lecture Notes - Lecture 4: Mathematical Proof, Language Of Mathematics, If And Only If
Document Summary
Week 2: lectures notes. Textbook: laura taalman, peter kohn: calculus, single variable,1e. A mathematical proof is a logical argument. Every theorem in this course can be proved with the use of previous theorems or definitions. In mathematics we cannot make conclusion based on our intuition. We have to use only proved theorems and true definitions to make every statement mathematically and logically sound. In mathematics we build up theories only on foundation of previous theorems and definitions. In the process of proving we"ll need to state if a property. True all the time , some of the time , at least ones , non of thee time . Logical quantifiers make such statements mathematically precise. For all ( ex: for all x, property p" means that property p holds for all values of x) The statement in the form if a then b ( Means that whenever statement a is true, statement b is also true.
