Did We Just Become Best Friends?
When Martha was young, she decided to list all the positive integers in ascending order: . After listing out millions and millions of these numbers, she found that there exists a positive integer that is both odd and even. Is it possible for Martha to find such a number?
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1 solution
An even number is divisible by 2 while an odd number is not. A number cannot be both divisible and indivisible by a number.
Assume that it is possible.
Let the number be n, we have n = 2 m and n = 2 k − 1 for some positive integers n,k.
We have 2 m = 2 k − 1 or k − m = 2 1 . As both n,k are integers their difference also must be an integer but 2 1 is not.
Contradiction.