In proof questions, what can any odd number be written as?

2 years ago


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Damaris Effertz

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Ante R Verified Sherpa Tutor āœ“

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An odd number is a number indivisible by 2.

Therefore, an odd number could be written like this:

x is odd if x = 2n-1, nāˆˆā„•.

This basically means that x is equal to twice some number n (where n is a natural number), with 1 subtracted. This makes x an odd number because 2 times any natural number is an even number (so 2n is always an even number), and 1 subtracted from any even number is an odd number; therefore x = 2n-1 is odd.

If that is how you define x, you can then use it in your proof as any odd number.

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