Find the Error in the Following Proof of This "Theorem $' n = n + 1 '$

question 8

Short Answer

Find the error in the following proof of this "theorem":
"Theorem: Every positive integer equals the next largest positive integer."
"Proof: Let P(n) be the proposition $' n = n + 1 '$
To show that $P ( k ) \rightarrow P ( k + 1 )$ assume that P(k) is true for some k , so that k=k+1 . Add 1 to both sides of this equation to obtain k+1=k+2 , which is P(k+1) . Therefore $P ( k ) \rightarrow P ( k + 1 )$ is true. Hence P(n) is true for all positive integers n . "

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Definitions:

Arguments

Involves presenting reasons or evidence to support or oppose an idea, action, or theory. It is a fundamental aspect of critical thinking and discourse.

Merit

The quality of being particularly good or worthy, especially so as to deserve praise or reward.

Cerebral Asymmetry

The uneven distribution and specialization of functions in the two hemispheres of the brain.

Right- and Left-hemisphere

Refers to the two halves of the human brain, each responsible for different functions; the left hemisphere is often associated with logical reasoning and language, while the right hemisphere is associated with creative and intuitive processes.