Show an informal proof to show that the following conjecture is true
Conjecture: The sum of an odd number and an even number is an odd number
Stacey Warren - Expert brainly.com
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I mostly don't really know how to type a informal proof.
Think of the integers.
... , -3, -2, -1, 0, 1, 2, 3, ...
Some integers are even, and some are odd.
If you multiply every integer by 2, are the products odd or even?
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... , 2(-3), 2(-2), 2(-1), 2(0), 2(1), 2(2), 2(3), ...
are all even
Since 2 times each integer is an even integer, we can write
For every integer n, 2n is an even integer.
Then by the same token, we can write
For every integer n, 2n + 1 is an odd integer.
I just really don't understand how to prove that. with an informal proof
We're getting there.
So far do you understand that
for every integer, n, 2n is an even integer, and
for every integer n, 2n + 1 is an odd integer?
Now let's add the numbers.
What is (2n + 1) + (2n) ?
(2n + 1) + (2n) =
= 2n + 1 + 2n
= 4n + 1
= 2(2n) + 1
Since for every integer n, 2n is an even integer, then 2(2n) must be even.
Therefore, 2(2n) + 1 = 4n + 1 is odd.