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Write the definition of a field and prove that (Q₁ +₁ •) Satisfies (iii) and (ix)

Write the definition of a field and prove that (Q₁ +₁ •) Satisfies (iii) and (ix)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Write the definition of a definition of a field and prove that (Q₁ +₁.) Satisfies (iii) and (ix)
Transcribed Image Text:Write the definition of a definition of a field and prove that (Q₁ +₁.) Satisfies (iii) and (ix)
A field is a set I with 2 binary operations, set I with +, •, such that if x, y, ZEI then (i) x + y Ex (ii) x+y = y +x (iii) x + (y+z) = (x+y)+2 (iv) 3 an identity for + usually denoted by o Such that 0 + x = x (v) 3 an inverse denoted -x such that x+(-x) = 0 (vi) xoy (denoted also) xy or (x) (y) or (x). (y) EI (vii) xy = yx (viii) x (yz) = (xy) z (√√√x) (x+y) z = x² + y² (x) 1x = x x(y +z) = (y+z)x = yx+zx= xy + x z Arrige setle Ex Q = Eall rational numbers (Q₁ +₁ •) is a field
Transcribed Image Text:A field is a set I with 2 binary operations, set I with +, •, such that if x, y, ZEI then (i) x + y Ex (ii) x+y = y +x (iii) x + (y+z) = (x+y)+2 (iv) 3 an identity for + usually denoted by o Such that 0 + x = x (v) 3 an inverse denoted -x such that x+(-x) = 0 (vi) xoy (denoted also) xy or (x) (y) or (x). (y) EI (vii) xy = yx (viii) x (yz) = (xy) z (√√√x) (x+y) z = x² + y² (x) 1x = x x(y +z) = (y+z)x = yx+zx= xy + x z Arrige setle Ex Q = Eall rational numbers (Q₁ +₁ •) is a field
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