What Is Wrong with the Following Proof That Every Positive $P ( n )$

question 3

Short Answer

What is wrong with the following proof that every positive integer equals the next larger positive integer? "Proof." Let $P ( n )$ be the proposition that $n = n + 1$ . Assume that $P ( k )$ is true, so that $k = k + 1$ . Add 1 to both sides of this equation to obtain $k + 1 = k + 2$ . Since this is the statement $P ( k + 1 )$ , it follows that $P ( n )$ is true for all positive integers $n$ .

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Definitions:

α

Represents the level of significance in hypothesis testing, often denoting the probability of making a type I error.

SSB

A statistical term that can stand for Sum of Squares Between groups, measuring the variability among group means in an analysis of variance.

SSE

Sum of Squared Errors, a measure used in statistics to show the dispersion of data points from their mean values.

Randomized Block Experiment

A statistical experiment design that aims to reduce variation among experimental units by grouping them into blocks based on certain characteristics before applying different treatments.