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2.7.5(1) Let R, and R2 be ordered fields that satisfy the Least Upper Bound Property, and let p: R1 → R2 be a function. Suppose that p(x + y) = p(x) + p(y) for all x, y e R1. (1) Prove that p(0) = 0

2.7.5(1) Let R, and R2 be ordered fields that satisfy the Least Upper Bound Property, and let p: R1 → R2 be a function. Suppose that p(x + y) = p(x) + p(y) for all x, y e R1. (1) Prove that p(0) = 0

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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2.7.5(1)

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**2.7.5(1)** Let \( R_1 \) and \( R_2 \) be ordered fields that satisfy the Least Upper Bound Property, and let \( p: R_1 \rightarrow R_2 \) be a function. Suppose that \( p(x+y) = p(x) + p(y) \) for all \( x, y \in R_1 \). (1) Prove that \( p(0) = 0 \).
Transcribed Image Text:**2.7.5(1)** Let \( R_1 \) and \( R_2 \) be ordered fields that satisfy the Least Upper Bound Property, and let \( p: R_1 \rightarrow R_2 \) be a function. Suppose that \( p(x+y) = p(x) + p(y) \) for all \( x, y \in R_1 \). (1) Prove that \( p(0) = 0 \).
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