Is there a proof or way of proving that all even numbers (taking into account the definition of an even number as [tex]n=2k[/tex]) end in 0,2,4,6, or 8?
An explanation such as this is alright for proving that an integer [tex]n[/tex] is even if [tex]n=2k[/tex], for some integer [tex] k.[/tex] Thus, we have to use our knowledge of even numbers to say that they end in an integer that is divisible by 2. A satisfactory explanation, no doubt, just not what I'm looking for.Rewrite n as 10a+b, where 0<=b<10.
Then n is even means 2 divides 10a+b, i.e. 2 divides b (let 10a+b=2k and solve for b). Hence b=0,2,4,6,8