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Activity: Rational Exponents and Equations with Radicals
... the rational numbers: This set consists of all fractions of integers m/n, where n 6= 0. Two fractions a/b and m/n represent the same rational number if an = bm. For example, 2/3 and 10/15 represent the same rational number since 2(15) = 3(30). the real numbers: This consists of the sets of all lengt ...
... the rational numbers: This set consists of all fractions of integers m/n, where n 6= 0. Two fractions a/b and m/n represent the same rational number if an = bm. For example, 2/3 and 10/15 represent the same rational number since 2(15) = 3(30). the real numbers: This consists of the sets of all lengt ...
Addition of polynomials Multiplication of polynomials
... Irreducible polynomials in R[x] Definition 9. A non-constant polynomial p(x) ∈ R[x] is reducible in R[x] if it can be factorised as p(x) = a(x)b(x), where a(x), b(x) ∈ R[x] with deg a(x) < deg p(x) and deg b(x) < deg p(x). It is irreducible in R if it is not reducible in R[x]. When we say that a pol ...
... Irreducible polynomials in R[x] Definition 9. A non-constant polynomial p(x) ∈ R[x] is reducible in R[x] if it can be factorised as p(x) = a(x)b(x), where a(x), b(x) ∈ R[x] with deg a(x) < deg p(x) and deg b(x) < deg p(x). It is irreducible in R if it is not reducible in R[x]. When we say that a pol ...
APM 504 - PS7 Solutions 3.4) Suppose that X1 and X2 are
... in which case there is a sequence hn ↓ 0 and numbers e > d > c such that ψ(hn ) > e for all n. Furthermore, since ψ is continuous on R/{0}, there exist numbers ln < rn with ln → 0 such that for every n ≥ 1, ψ(t) > d for all t ∈ In ≡ (ln , rn ). In light of (?), there can be no t > 0 such that the s ...
... in which case there is a sequence hn ↓ 0 and numbers e > d > c such that ψ(hn ) > e for all n. Furthermore, since ψ is continuous on R/{0}, there exist numbers ln < rn with ln → 0 such that for every n ≥ 1, ψ(t) > d for all t ∈ In ≡ (ln , rn ). In light of (?), there can be no t > 0 such that the s ...
