Let S = C[0,1] be the set of real-valued continuous functions defined on the closed interval [0, 1], where we definef+ g and fg, as usual, by (f+ g)(x) = f(x) + g(x) and (fg)(x) = f(x)g(x). Let O and I be the constant functions 0 and 1, respectively. Show that (a) (S,+,) is a commutative ring with unity. S has nonzero zero divisors. (b)
Let S = C[0,1] be the set of real-valued continuous functions defined on the closed interval [0, 1], where we definef+ g and fg, as usual, by (f+ g)(x) = f(x) + g(x) and (fg)(x) = f(x)g(x). Let O and I be the constant functions 0 and 1, respectively. Show that (a) (S,+,) is a commutative ring with unity. S has nonzero zero divisors. (b)
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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