Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form `2q+1`, where q is some integer.
Text Solution
AI Generated Solution
To show that every positive even integer is of the form \(2q\) and that every positive odd integer is of the form \(2q + 1\), where \(q\) is some integer, we can follow these steps:
### Step 1: Define a Positive Integer
Let \(a\) be any positive integer. We need to determine whether \(a\) is even or odd.
### Step 2: Division by 2
When we divide \(a\) by \(2\), we can express \(a\) in the form:
\[
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