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Question

Show that every positive even integer is of the form $$2n$$ and every positive odd integer is of the form $$2n+1$$.


Solution

By the definition of even number, every even number is divisble by $$2$$.
$$E=2n$$ where $$n \in N$$.
By the definition of odd number, every odd number is not divisble by $$2$$. The only possible remainder when divided with $$2$$ is $$1$$.
Hence odd numbers can be of the form $$2n+1$$ where $$n$$ is the quotient when divided with $$2$$.
$$O=2n+1$$ where $$n \in W$$

Mathematics

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