MAT102H5 Lecture 8: Ch. 2 Language and Proofs
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MAT102H5 Full Course Notes
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Document Summary
In order to communicate and argue in mathematics properly, we need to use the language of mathematics (i. e its syntax) correctly. Understand various components of the language and put them together in a meaningful way. We will see the spoken language (i. e english), but in a more formal and precise way. What is the language of mathematics made of: mathematics statement. A mathematical statement is a sentence which can be either true or false. The square root of 9 is 3 this is a true statement. Z q is a true statement. is empty is a false statement. f : r r , f (x)=x2 ,isbounded is a false statement. If x is assigned a value, then we get a statement: quantifiers: for all , every , there is etc, variables/parameters/formulas: x,y,g,x+y^2 , logical connectives: not , and , or , if ,then , if and only if For all x r , we have x2>0 is a false statement.
