Handwritten Stuff

Handwritten Stuff - RIK SENGUPTA Professor Delia Graff Fara...

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RIK SENGUPTA Professor Delia Graff Fara Philosophy 201 Homework 4 EXERCISE 5.12 The justification behind introducing this claim in our proof is that a number can either be expressed in the form p/q, where p and q are integers (q is non-zero), or it cannot be expressed in that form. If it can be expressed as p/q, then it is rational, otherwise it is irrational. So every real number is either rational or irrational. We use the fact that 2 2 is a real number, because it is a point on the real line (this can also be derived from Cauchy sequences). Now, a real number is either rational or irrational. So 2 2 is also either rational or irrational, a fact which we will use in our proof by cases method. EXERCISE 5.15 So we have, b is a tetrahedron, and c is a cube. We know either c is larger than b , or else they are identical, so that one of the two conditions must be true. But, using proof by cases, since b is a tetrahedron and c is a cube, they are by definition not identical. This means that

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Handwritten Stuff - RIK SENGUPTA Professor Delia Graff Fara...

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