Question

show that every positive even integer is of the form 2m and that every positive odd integer is of the form (2m+1), where m is some integer.​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let n be an arbitrary positive integer.

On dividing n by 2,

Assume m be the quotient.

And r be the remainder.

n = 2m + r,

where 0 ≤ r < 2.

Therefore,

n = 2m or (2m + 1), for some integer m.

Case 1.

in this case, n is clearly even.

Case 2.

In this case, n is clearly odd.

Hence, every positive even integer is of the form 2m and every positive odd integer is of the form (2m + 1) for some integer m.