"Proof": Take any group of n cats, where n = 1, 2, ... We need to prove that all cats in this group have the same color. This is an obvious statement for n = 1. Inductive step: Assume that the statement holds for k. We need to prove it for k + 1. Consider a group of k + 1 cats. Label them by numbers from 1 to k+1. By the inductive assumption, cats 1, ..., k have the same color. Similarly, by the inductive assumption cats 2, ..., k +1 have the same color, since there are k of them. Since these two sets intersect, all k + 1 cats have the same color. Where is the error in this proof?
"Proof": Take any group of n cats, where n = 1, 2, ... We need to prove that all cats in this group have the same color. This is an obvious statement for n = 1. Inductive step: Assume that the statement holds for k. We need to prove it for k + 1. Consider a group of k + 1 cats. Label them by numbers from 1 to k+1. By the inductive assumption, cats 1, ..., k have the same color. Similarly, by the inductive assumption cats 2, ..., k +1 have the same color, since there are k of them. Since these two sets intersect, all k + 1 cats have the same color. Where is the error in this proof?
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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