Problem 8. We wish to do formal addition and subtraction with a set of three stones. For this purpose we shall model the stones by three letters S1, S2 and S3. Our aim is to develop a for- mal algebra of stones that allows us to do addition and subtraction as we do with integers, so expressions like S1 + S2, or -5 × S3 should be possible. (a) What could be a sensible intended interpretation of S1 + S2? (b) What would be a sensible interpretation of -5 × S3? (c) Develop ideas how such a formal algebra could be defined and implemented. (d) Can you solve linear and quadratic equations in your formal algebra of stones? Discuss. (e) What relationship can you draw from your formal algebra of stones to working with numbers like the reals, say?

Problem 8. We wish to do formal addition and subtraction with a set of three stones. For this purpose we shall model the stones by three letters S1, S2 and S3. Our aim is to develop a for- mal algebra of stones that allows us to do addition and subtraction as we do with integers, so expressions like S1 + S2, or -5 × S3 should be possible. (a) What could be a sensible intended interpretation of S1 + S2? (b) What would be a sensible interpretation of -5 × S3? (c) Develop ideas how such a formal algebra could be defined and implemented. (d) Can you solve linear and quadratic equations in your formal algebra of stones? Discuss. (e) What relationship can you draw from your formal algebra of stones to working with numbers like the reals, say?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 92E

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