Rest of Geom Chapter1 Part4

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This next section is called "Inductive' Verses 'Deductive' Reasoning. In accumulating consecutive odd integers beginning with 1; 1+3 =4 1+3+5 =9 1+3+5+7 =16 1+3+5+7+9 =25 "Do you notice a pattern? It appears that the sum of consecutive of consecutive odd integers beginning with 1, will always be a 'perfect square'.(a 'perfect square' is a number that can be expressed as the product of two identical numbers.)If, on the basis of this evidence, we now conclude that this relationship will always be true, regardless of how many terms are added, we have engaged in 'inductive reasoning'. 'Inductive reasoning' involves examining a few examples, observing a pattern, and then assuming that the pattern never ends. 'Inductive reasoning' is not a valid method of proof, although it often suggests statements that can be proved by other methods. 'Deductive Reasoning' may be considered to be the opposite of 'inducive reasoning'. Rather than begin with a few specific instances as is common with inductive processes, 'deductive reasoning' uses accepted 'facts'(i.e., undefined terms, defined terms, postulates, and previously established theorems) to reason in a step-by-step fashion until a desired conclusion is reached." An example is used "Assume the following two postulates are true.(1) All last names that have seven letters with no vowels are the names of Martians. (2) All Martian is s are 3 feet tall. Prove that Mr. Xhzftir is 3 feet tall." Solution a two column format should prove it true but considering the facts are not true because not all 7 letter with no vowels is always Martians and not all people 3 feet tall are Martians, therefore this proof cannot be true. Reasons Statements 1. Given The name is Xhzftir. 2. All last names that have seven letters Mr. Xhzftir is a Martian, cannot with no vowels are the names of e true. Martians. (Which in this case actually Mr. Xhzftir is 3 feet tall cannot cannot be a postulate but it says it is. be proof either because the postulate is not true. Therefore, make sure your postulates are true, and all the facts add up. (a Solution is in lesson part 4b.)